date : 19-04-15 vibrant academy

REVIEW TEST–1 (MEGA PHASE-I COURSE-2016)JEE Mains

Time : 3 Hours Maximum Marks : 360Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

INSTRUCTIONSA. General :

1. This booklet is your Question Paper containing 90 questions. The booklet has32 pages.

2. The question paper CODE is printed on the right hand top corner of this sheet andon the back page (page no. 32) of this booklet.

3. The question paper contains 4 blank pages for your rough work. No additional sheetswill be provided for rough work.

4. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers andelectronic gadgets in any form are not allowed to be carried inside the examination hall.

5. Fill in the boxes provided below on this page and also write your Name and VARoll No. in the space provided on the back page (page no. 32) of this booklet.

6. The answer sheet, a machine-readable Objective Response Sheet (ORS), is providedseparately.

7. DO NOT TAMPER WITH / MUTILATE THE ORS OR THE BOOKLET.

8. Do not open the question-paper booklet before being instructed to do so by the invigilators.

B. Question paper format Read the instructions printed on the back page

C. Marking scheme (page no. 32) of this booklet.

Name of the candidate VA Roll Number

I have read all the instructions and I have verified all the information filled shall abide by them. in by the candidate.

.......................................................... ............................................................ Signature of the Candidate Signature of the invigilator

VIBRANT ACADEMY(India) Private Limited

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CODE - A

USEFUL DATAAtomic weights: H = 1, He = 4, Li = 7, g = 10 m/s2 , B = 11, C = 12, N = 14, O = 16, F = 19, Ne = 20, Na = 23,Mg = 24, Al = 27, P = 31, S = 32, Cl = 35.5, K = 39, Ca = 40, Ar = 40 , Ti = 48, Cr = 52, Mn = 55, Fe = 56,Co = 59, Cu = 63.5, Zn = 65.5, Br = 80, Mo = 96, Ag = 108, I = 127, Ba = 137, U = 238

DATE : 19-04-15

Vibrant Academy (I) Pvt. Ltd. "A-14(A)" Road No.1, Indraprastha Industrial Area, Kota (Raj.) Ph. 0744-2423406 [RT-1,JM-A-2]

PART I : MATHEMATICSSingle Correct Choice Type

This section contains 30 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONLY ONE is correct.

1. Let f(x) = tan–1 (sin x + cos x) then f (0) equals

(A) 12

(B) 0 (C) 1 (D) Does not exist

2. Let f : R R be a function defined by f(x) = min {x + 1, |x| + 1}. Then which of the following is true ?(A) f(x) 1 x R (B) f(x) is not differentiable at x = 0.(C) f(x) is not differentiable at x = 1. (D) f(x) is differentiable everywhere.

3. Let f(x) = 2x1 2– ; x 0x e – 1 ; x 0

The value of for which f(x) is continuous at x = 0(A) 0 (B) 1 (C) –1 (D) No value

4. If f : R R satisfies f(x) f(y) = f(xy) + x + y x, y R, (f(1) –1) then f(1) =(A) 0 (B) 1 (C) 2 (D) None of these

Space For Rough Work



MATHEMATICS

5. The number of points of discontinuity of f(x) = [tan x [cot x]] ; x ,12 2

.

(where [.] represent greatest integer function).(A) 0 (B) 1 (C) 2 (D) More than 2

6. Let f : (0, ) R and g : (0, ) R be two functions where g(x) = x + 1x

. If 9 < f(x).g(x) < 99 x > 0 then

xlim

f(x) is(A) 0 (B) 54 (C) 100 (D) Can not be determined

7.

2xe

x 0

d e – elimdx x

is

(A) 0 (B) e (C) e2 (D) –e

8. Let f(x) = x|x|, g(x) = sin x and h(x) = (gof) (x). Then(A) h(x) is not differentiable at x = 0.(B) h(x) is differentiable at x = 0 but h(x) is discontinuous at x = 0.(C) h(x) is continuous at x = 0 but not differentiable at x = 0.(D) h(x) is differentiable at x = 0.



MATHEMATICS9. The figure shows an isosceles triangle ABC with B =C. The bisector of angle B intersects the side AC at

the point P. Suppose that BC remains fixed but the altitude AM approaches 0, so that A M (mid-point ofBC). Limiting value of BP, is

(A) 3a

(B) 2a

MCB

A

P

(C) 3a2

(D) 4a3

where a is fixed side BC.

10. If f(x) = 22 cos x – 1 ; x

( – x)k ; x

is continuous at x = , then k equals

(A) 0 (B) 12

(C) 2 (D) 14

11. Let f : R R be a function such that |f(x)| x2, x R. Then at x = 0, f is(A) Continuous but not differentiable. (B) Continuous as well as differentiable.(C) Neither continuous nor differentiable. (D) Differentiable but not continuous.

12. Let f(x) = x 5 ; x 2x – 2

1 ; x 2

Number of points of discontinuity of f(f(x)) is/are(A) 0 (B) 1 (C) 2 (D) 3



MATHEMATICS

13. Let f : [0, ] R be defined as f(x) = 2

sinx ; if x is irrational

tan x ; if x is rational

The number of points in [0, ] at which f is continuous.(A) 6 (B) 4 (C) 2 (D) 0

14. Let f(x) = 3x10 – 7x8 + 5x6 – 21x3 + 3x2 – 7

h5sin)1(f–)h–1(f

h3hlim26524

0h

(A) 1 (B) 2 (C) 3 (D) –3

15. If f(x) has isolated point of discontinuity at x = a such that |f(x)| is continuous at x = a then

(A) ax

lim

f(x) does not exist (B) ax

lim

f(x) + f(a) = 0

(C) f(a) = 0 (D) None of these

16. Polynomial function f(x) = x3 – x2 + 1 has a value zero for x = c, then c must lie

(A) [–1, 0] (B) [0, 1] (C)

23,1 (D) None of these



MATHEMATICS

17. )x(coscos–)x(tantanLim 1–

1–

2x

–

(A) –1 (B) 1 (C) Does not exist (D) None of these

18. Number of points of discontinuity of

2x

5x)x(f in x [0, 100] is/are (where [·] denotes greatest

integer function and {·} denotes fractional part function)(A) 50 (B) 51 (C) 52 (D) 55

19. If f(x) = [2 + 7 sin x], 0 < x < , number of points at which the function is non derivable is(A) 13 (B) 7 (C) 6 (D) 1

20. Let f : [1, 10] Q be a continuous function and f(1) = 10 then f(10) is equal to

(A) 101

(B) 10 (C) 1 (D) can't be obtained



MATHEMATICS

21.

xsec

2x

)x(sinLim

(A) e (B) e–1 (C) 1 (D) does not exist

22.

1–)nx(

1)nx(LimLim n

n

nex

(A) 1 (B) –1 (C) 0 (D) Does not exist

23.

1–3

41–

3

2

1–21x x–x1–x3

x–1xx3–1–

xx4Lim

(A) 1 (B) 2 (C) 3 (D) 0


MATHEMATICS


24.

)]x[cos(sin0x

|xsin|Lim ..........., where [·] denotes greatest integer function

(A) Does not exist (B) 0 (C) e (D) 1

25. If f(2010) = 2

, f(x) = f(2x) x R and f(x) is continuous for x R, find the value of

)x(sin))x(fcos(–))x(fcos(

lim 2

3

0x is

(A) 41

(B) 1 (C) 0 (D) None of these

26. Let f(x) = [x] and g(x) = 0 x I = x2 otherwise

Then (where [·] represent greatest integer function)

(A) fog is differentiable funciton (B) fog is differentiable on )0(R

(C) gof is not continuous only at x = 0 (D) gof (2) = 1



MATHEMATICS27. Function f(x) = |x – 3| x 1

= 4

132x3

4x2

x < 1 Then

Which of the following option is INCORRECT(A) Continuous at x = 1 (B) Continuous at x = 3(C) Differentiable at x = 1 (D) Differentiable at x = 3

28. If 2 3 nx x x xy(n) e . e . e ....... e , 0 < x < 1 then dx

))n(y(dlimn

at 21x is equal to

(A) e (B) 4e (C) 2e (D) 3e

29. If x

x11y

then y'(2) is equal to

(A)

23log

31–

49

(B)

23log

31–

94

(C)

23log–

31–

49

(D) None of these

30. Given a function g(x) which has derivative g'(x) for all x satisfying g'(0) = 2 and g(x + y) = ey . g(x) + ex . g(y)for all x, y R . g(5) = 32 then the value of g'(5)– 2e5 is equal to(A) 5 (B) 25 (C) 32 (D) None of these


PART II : PHYSICSSingle Correct Choice Type


31. An observer 'O' at an accelerated trolley observes a projectile Q of mass 5 kg moving under uniform gravita-

tional field of earth acting towards negative z-axis. He observes the momentum P

of the projectile Q as2ˆ ˆ ˆP 15ti – 10t j – 50tk

(kg m/s), where t denotes time in second. Find the acceleration of the trolley at t = 2

sec. (Take g = 10 m/s2)

(A) 2ˆ ˆ ˆ(6i – 8 j – 20k) m / s (B) 2ˆ ˆ(3i – 8 j )m / s

(C) 2ˆ ˆ(–3i – 8 j )m / s (D) 2ˆ ˆ(–3i 8 j )m / s

32. A plane thick wall having uniform surface temperature along planes are 0ºK and T0ºK (T0 = 300K) at x = 0 andx = x0 respectively. Thermal conductivity K varies linearly with temperature asK = K0 (1 + T) the temperature of wall at the plane x = 2x0 is approximately : (where T is in kelvin)(A) 300 K (B) 400 K (C) 425 K (D) 450 K

33. a projectile is fired with velocity v at angle of with horizontal. What would be the radius of curvature of pathat instant when rate of change of speed of projectile is minimum ?

(A) 2 2v cos

g

(B) 2v

gcos(C)

2v cosg

(D)

2

2v

gcos



PHYSICS


34. A ball of mass 1 kg attached with string of length 10 m is free to rotate on smooth horizontal plane is

subjected to constant force of ˆ ˆ– 2 i j N. What should be the minimum velocity of projection at position

shown in figure, so that it complete full revolution ?(A) 10 ms–1

(B) –12 5 ms

(C) –14 5 ms45º

X

V

Y

10m

(D) 6 ms–1

35. A man with least distance of clear vision equals to 30 cm, reads a book with small print using a magnifyingglass (simple microscope), a thin convex lens of focal length 15 cm. What is the maximum magnifying powerpossible using the above simple microscope ?(A) 1.5 (B) 2.5 (C) 3 (D) 3.5

36. If VA = 10 m/sec, what would be the velocity of C ? 1 = 30º, 2 = 60º. B is very heavy and remains on ground.

(A) 103

m/sec

(B) –110 3 ms

ABC 10 m/sec12

(C) 10 ms–1

(D) –15 3 ms


PHYSICS


37. A light ray is incident on a plane mirror M. The mirror is rotated in direction as shown in figure by an arrow atfrequency (9/) revolution/sec. The light reflected by the mirror is received on the wall W at a distance of 10m from axis of rotation. Speed of the spot on wall when angle of incident = 37º is(A) 10 m/sec(B) 1000 m/sec(C) 360 m/sec(D) 500 m/sec

38. Initially spring is relaxed and m1 is released from rest. When m1 come to rest for a moment string AB is cutat the same moment. Find the acceleration of m2 just after cutting the thread.

(A) a = 1

2

m–1 g

m

(B) a = 1

2

2m– 1 g

m

(C) a = 1

2

m– 1 g

2m

(D) a = 1

2

3m– 1 g

m

39. A compound microscope consist of an objective lens of focal length 2.0 cm, and an eye piece of focal length6.25 cm, separated by a distance of 15 cm. How far from the objective should an object be placed in order toobtain the final image at least distance of distinct vision (25 cm).(A) 1.5 cm (B) 2.5 cm (C) 3.0 cm (D) 3.5 cm


PHYSICS


40. A convex lens is made of two different materials having radius of curvature of surface A and surface B as 25cm and 24 cm respectively. The effective focal length of lens is

(A) 75/4 cm

(B) 75 cm

A B

1=1.5 2=1.8(C) 50 cm

(D) 30 cm

41. Potential energy of a system of two particles is U = K ,r

where r is the distance between them. If both the

particles are set free,

(A) r will increase if K is positive.

(B) r will increase if K is negative.

(C) r may decrease or increase, it does not depends on sign of K.

(D) From given information we can not conclude whether r will increase or decrease.

42. One mole of an ideal gas undergoes a process AB where A (2P0, V0) & B (1.5 P0, 1.5 V0). The process is

shown in the PV diagram. The temperature of the gas (select the WRONG statement) :

(A) Increases and then decreases.

(B) Only increases.

(C) Has a maximum value of 0 0P V94 R

A

B

P

V

(D) Is more at B than at A.


PHYSICS


43. A light ray parallel to x-axis is incident on a parabolic concave mirror in XY plane. The focus of this parabolais at (1, 0). The unit vector along the reflected ray will be

(A) j

(B) ˆ– j

(C) ˆ ˆi 4 j

17

(D) ˆ– i

44. Area of triangle formed by S and its two images is

(A) 23 3 m (B) 23 3 m4

120º2m

S

\\\\\\

(C) 24 m

3 3 (D) Can't be determined

45. On one boundary of a swimming pool, there is a person at point A, whose speed of running on ground

(boundary) is 10 ms–1, while that of swimming is 6 ms–1. He has to reach a point B in the swimming pool.

The distance covered on the boundary so that the time required to reach the point B in the pool is minimum, is

4m

10mA

SwimmingPool B

(A) 10 m (B) 6 m (C) 7 m (D) 116 m

46. For a process, relation between temperature and volume is TV3 = constant. If a monatomic gas follows thisprocess, then find the molar specific heat for this process [R is a gas constant].

(A) 7R6 (B)

R3 (C)

11R6 (D) zero


PHYSICS


47. The potential energy of a 1 kg particle free to move along the x-axis is given by U(x) = 4 2x x

4 2

J. The total

mechanical energy of the particle is 2J. Then, the maximum speed of particle (in m/s) is

(A) 12

(B) 2 (C) 32

(D) 2

48. In the figure shown, the spring constant is K. The mass of the upper discis m and that of the lower disc is 3m. The upper block is depressed downfrom its equilibrium position by a distance = 5mg/K and released att = 0. Find the velocity of ‘m’ when normal reaction on 3m is mg.(A) zero (B) g[m/K]1/2 (C) 2g[m/K]1/2 (D) 4g[m/K]1/2

49. Two spherical mirror, one convex and other concave, each of same radius of curvature R are arrangedcoaxially at a distance 2R from each other. A small circle of radius a is drawn on the convex mirror near thepole as shown in figure. The radius of 2nd image (taking the first reflection at the concave mirror, then the

reflection at the convex mirror) of the circle is 3a

30 x

, then value of x is

\\\\\\\\\\\\ \\\\\\\\\\\\\\

\\\\\\\\\\ \\\\\\\\\\\\\\\

2R

M1 M2

(A) 1 (B) 2 (C) 3 (D) 4


PHYSICS


50. A particle moves in a circle with a uniform speed, when it goes from a point A to a diametrically opposite point

B, the momentum of the particle changes by A BˆP – P 2kg m / s( j)

and the centripetal force acting on it

changes by A BˆF – F 8N(i)

where ˆ ˆi, j are unit vectors. Then the angular velocity (in rad/s) of the particle is

(A) 1 (B) 2 (C) 4 (D) 8

51. The distance between object and screen is 96 cm. The ratio of length of two images formed by a convex lensplaced between them is 4.84. The focal length f is nearly(A) 22 cm (B) 20.6 cm (C) 24 cm (D) 24.2 cm

52. A ray of light incident normally on the horizontal face of the slab and just fail toemerge from the diagonal face of the prism. If prism angle is 30°, refractive indexof the prism is

(A) 2 (B) 2(C) slightly greater than 2 (D) slightly less than 2

53. For a glass prism of R.. = 1.732 the angle of minimum deviation is equal to the angle of the prism. The angleof the prism in degrees is nearly(A) 80 (B) 30 (C) 60 (D) 90


PHYSICS


54. The limiting angle of incidence of a ray that can be transmitted by an equilateral prism of 73

will be

(A) 60° (B) 30° (C) 45° (D) None of these

55. A point object is moving on the principle axis of concave mirror of focal length 24 cm towards it. When it is ata distance of 60 cm from the mirror, its velocity is 9 cm/s. What is the velocity of its image in cm/s at thatinstant ?(A) 5 cm/s towards the mirror (B) 4 cm/s towards the mirror(C) 4 cm/s away from the mirror (D) 9 cm/s away from the mirror

56. Two particles instantaneously at points A and B respectively 4.5 metres apart are moving with uniformvelocities, the former towards B at 1.5 m/sec and the latter perpendicular to AB at 1.125 m/sec. The instantwhen they are nearest.

(A) 231 sec25 (B)

41142

sec (C) 232 sec27

(D) none of these

57. A ray incident at a point at an angle of incidence of 60° enters a glass sphere of = 3 and is reflected and

refracted at the farther surface of the sphere. The angle between the reflected and refracted rays at thissurface is(A) 50° (B) 90° (C) 60° (D) 40°



PHYSICS

58. A spherical glass bulb of diameter d is filled with water 43

. The bulb is viewed along its horizontal

diameter. What is the apparent diameter? (Neglect the thickness of glass)

(A) 2d (B) 3d2

(C) d2

(D) 7 d4

59. An object O is located 40 cm from the first of two thin converging lenses (each of focal length 20 cm), asshown in the figure below. If speed of the right lens is 7 cm/s rightwards, speed of final image is

4x7

cm/s at the instant shown, find the value of x.

20 cm

40 cmO

v = 7 cm/s

f = 20 cm1 f = 20 cm2

(A) 1.5 (B) 2.5 (C) 3.5 (D) 3

60. A bead of mass m is tied at one end of a spring of spring constant k = mg/R and unstretched length R/2 andother end to fixed point O, as shown in the figure. The smooth semicircular wire frame is fixed in verticalplane. The normal reaction between bead and wire just before it reaches the lowest point is N. Find the ratioof N to weight mg of the bead. (Radius of semicircular frame is R)

R

R/2O

k = mg / R

•

m

(A) 6 (B) 6.25 (C) 11.2 (D) 16


PART III : CHEMISTRYSingle Correct Choice Type


61. Maximum number of plane of symmetry possible in

(A)

Cl

(B)

Cl

Cl

(C)

ClCl

(D)

Cl

Cl

62. In which of the following conversion both hybridisation as well as shape changes with respect to centralatom?

(A) CH3 C2H6 (B) NH3 4NH

(C) H2O H3O+ (D) All

63. Consider the following gaseous reaction where initial pressure of P(g) is 200 mmHgP(g) 3Q(g) + R(g)

After time t, the pressure of system increases by 450 mm Hg. Calculate the value of t (in second)?(Given : rate constant of reaction, k = 4.606 × 10–3 s–1, log2 = 0.3)(A) 600 (B) 300 (C) 50 (D) 5




CHEMISTRY64. Number of optically active tartaric acid is/are possible

(A) 1 (B) 2 (C) 3 (D) 4

65. 2X(g) + Y(g) + 3Z(g) Products

The rate equation of the above reaction is given by Rate = k[x] [y]0[z]2

Choose INCORRECT statement :(A) The rate of reaction is doubled by doubling the concentration of X(g) keeping other reactantsconcentration to be same.(B) The half life of Z(g) decreases by increasing its concentration.(C) If 50% of X(g) reacts in 10 sec. then 75% of X will react in 20 sec.(D) The rate of reaction decreases by reducing the concentration of Y(g) to half of original value.

66. Which of the following general formula represent to pyroxenes :

(A) 2n2 5 nSi O (B) 2n

3 nSiO (C) 44SiO (D) 6

2 7Si O

67.

Br

Br

O O Number of optically active isomer is/are

(A) 0 (B) 1 (C) 2 (D) 3



CHEMISTRY68. 20 V H2O2 solution is kept in the open vessel and is allowed to decompose by first order kinetics.

After 6 hours, 10 ml of this H2O2 sample was taken and diluted to 100 ml by adding water. 10 ml of thisdiluted solution requires 25 ml of 0.025 M KMnO4 in acidic medium for titration.Calculate the rate constant for the decomposition of H2O2. [Given : log102 = 0.3, log107 = 0.84](A) 0.22 hr–1 (B) 0.023 hr–1 (C) 0.175 hr–1 (D) 17.5 hr–1

69. Shortest O–O bond length is present in:(A) O2F2 (B) O2 (C) O2[BF4] (D) O3

70. Number of diastereomers possible for CH–CH3

CH3

(A) 1 (B) 2 (C) 4 (D) 0

71. Statement-I : H3BO3 (Boric acid) is a weak monobasic lewis acid.Statement-II : B–O bond length in H3BO3 is shorter than than of in its conjugate base (B(OH)4)

–

(A) Statement-1 is true, Statement-2 is true and Statement-2 is correct explanation for Statement-1(B) Statement-1 is true, Statement-2 is true and Statement-2 is NOT the correct explanation for Statement-1(C) Statement-1 is true, Statement-2 is false(D) Statement-1 is false, Statement-2 is true


CHEMISTRY


72. Quinones are good oxidising agents. In a cell reaction quinone converts itself into Hydroquinone as givenbelow :

||

||

O

O

|OH

|OH

p-Quinone Hydroquinone

The total number of electrons taken by each quinone molecule in the above process is(A) 6 (B) 2 (C) 1 (D) Can't be predicted

73. (1) (P) Plane of symmetry

(2)

Br

Br(Q) Meso compound

(3)O

O

O

O

CH3

CH3

(R) Number of possible diastereomers are zero

(4)

F F

Br Br

(S) C2 axis of symmetry

1 2 3 4(A) P S Q R(B) R Q P Q(C) P Q P R(D) R S Q Q



CHEMISTRY74. Which of the following property is different between NO and 2O

(A) sp mixing (B) Magnetic behaviour (C) Bond order (D) and -bond

75. At low pressure conditions the expression of compressibility factor for one mole of a real gas is given by :

(A) Z = a1

PRT (B) Z = 1 – 2)RT(z

aP(C) Z =

Pb1RT

(D) Z = ma V1

RT

76. Which conformer of butane are chiral in the given form

(1)

CH3

H

H H

H

CH3

(2)

CH3

H

H

H

H

CH3

(3)

CH3

H

H

CH3

HH

(4)

H

CH3

HH

CH3

H

(A) 1, 2 (B) 2, 3 (C) 2, 4 (D) 1, 3

77. Select the CORRECT statement regarding 22C molecular species.

(A) HOMO is Gerade (B) LUMO is Ungerade(C) SOMO is Ungerade (D) Both HOMO and LUMO and Gerade



CHEMISTRY78. If equal volume of oxygen gas and unknown gas take 2.0 and 4.0 minutes to effuse through a membrane

respectively. What is the molar mass of unknown gas ?(A) 8 g/mole (B) 64 g/mole (C) 128 g/mole (D) 306 g/mole

79. Which of the following molecule is not formed by involvement of co-ordinate bond(s).(A) Cl2O6 (B) I2Cl6 (C) Al2(NH2)6 (D) (NH4)2[SiF6]

80.3Cl /hv2

Additionreaction Product(x)

C H Cl6 6 6

Find the number of meso & optically active isomers possible for product(x) respectively(A) 2,7 (B) 3,6 (C) 8,2 (D) 7,2

81. Aqueous NH4NO2 decomposes according to the first order reaction :NH4NO2(aq) N2(g) + 2H2O()

At constant temperature and pressure, the volume of N2 collected after 20 minutes is 20 ml & after a verylong time is 40 ml. The rate constant for the reaction is [Given : log2 = 0.3010](A) 1.435 × 10–2 min–1 (B) 3.466 × 10–2 min–1 (C) 2.465 × 10–2 min–1 (D) 6.93 × 10–2 min–1



CHEMISTRY82. For following oxyanions :

S

O

O–O O–

x S

S

O–O O–

yz

Correct order of bond length is :(A) z > y > x (B) z > x > y (C) y > z > x (D) y > x > z

83. Identify the D or L configuration for the given 2 compounds respectively

OH H

CHO H

HO CH OH2 H

HOCHO

OH

H

CH OH2

(A) D, L (B) L, D (C) D, D (D) L, L

84. X Y : Initially the rate of reaction is 0.5 M hr–1. The initial conc. of X is 1.0 M. The degree of conversion ofX is maximum in one hour if reaction is (Given : e0.5 = 1.65)(A) Zero order reaction (B) First order reaction(C) Second order reaction (D) Data is not sufficient



CHEMISTRY

85. PCl

AlCl3Q

Hot KMnO4 , Product (Q) is

(A) COOH (B) COOH (C)

COOH

(D) COOH

86. For first order decomposition of N2O5(g) to give NO2(g) and O2(g) at constant temperature, which of thefollowing graph is correct.(Where : PO2

represents partial pressure of O2 gas and t1/2 represents half life of N2O5(g))

(A) (B) (C)

[N O ]52

d[O ]dt

2

(D)

87. Which pair of molecular species has same bond order as well as magnetic moment.

(A) B2, O2 (B) C2, O22– (C) S2, O2 (D) 2– 2

2 2N ,O



CHEMISTRY88. Which of the following preperation method for benzene is not correct

(A) 3HC CH Red hotFe tube (B)

Cr O – Al O2 3 2 3

600ºC

(C)

COOH

NaOH + CaO

(D)

Cl

NaDry ether

89. In an iodometric estimation, the following reactions occur

2Cu2+ + 4I– Cu2I2 + I2 ; I2 + 2Na2S2O3 2NaI + Na2S4O6

0.15 mole of CuSO4 was added to excess of KI solution and the liberated iodine required 1M of hyposolution. Used volume of hypo solution was :(A) 50 (B) 100 (C) 150 (D) 175

90. Which of the following nonmetal does not form dibasic oxyacid.(A) C (B) P (C) S (D) Cl


B. Question paper format :9. The question paper consists of 3 parts (Physics, Chemistry and Mathematics).

10. Parts contains 30 multiple choice questions. Each question has 4 choices (A), (B),(C) and (D) for its answer, out of which only one is correct.

C. Marking Scheme :

11. For each question in Parts, you will be awarded 4 marks if you have darkened onlythe bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. In all other cases, minus one (–1) mark will be awarded.


CODE - ADATE : 19-04-15

REVIEW TEST–2 (MEGA PHASE-I COURSE-2016)JEE Advance (Paper-1)



















CODE - A


DATE : 10-05-15

Vibrant Academy (I) Pvt. Ltd. "A-14(A)" Road No.1, Indraprastha Industrial Area, Kota (Raj.) Ph. 0744-2423406 [RT-2,P-1-A-2]

PART I : MATHEMATICSSECTION - I

Single Correct Choice TypeThis section contains 7 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONLY ONE is correct.

1. If a, b, c the sides of a ABC are in arithmatic progression in that order and a2 2 1 8

1 9 3 7 5 5 (2b) than

In radius of the ABC is

(A) 72

(B) 32

(C) 52

(D) 12

2. The product of the roots of the equation.

2

1 2x 1 1– x2 – x 2 x 3 x 0

x 1 x 1– x

(A) 2 (B) 1–2

(C) 12

(D) 1

3.3

4(x – 1) dx ,

(x 1) (x 1) equals to

(A) 14

ln (1 + x4) + 13 ln (1 + x3) + C (B)

14

ln (1 + x4) – 13 ln (1 + x3) + C

(C) 14

ln (1 + x4) – ln (1 + x) + C (D) 14

ln (1 + x4) + ln (1 + x) + C



MATHEMATICS

4. The value of dzdy

at x = e where y = ex ln2 x ; z = ln x is

(A) e(e + 2) (B) e2(1 + 2e) (C) ee(e + 2) (D) None of these

5. Suppose logab + logba = C. The smallest possible integral value of C for all a, b > 1 is(A) 4 (B) 3 (C) 2 (D) 1

6. Let A(4, 0) and B(0, 12) be two points in the plane. The locus of a point C such that the area of the triangleABC is 18 square units is :(A) (y + 3x + 12)2 = 81 (B) (y + 3x + 81)2 = 12(C) (y + 3x – 12)2 = 81 (D) (y + 3 x – 81)2 = 12

7. If f(x) = (2015 + x)n where x is a real variable and n be a positive integer, then the value of

(n–1)f "(0) f (0)f(0) f '(0) .......2 n – 1

is

(where f(n)(0) denotes nth derivative of f at x = 0).(A) (2015)n (B) (2015)n – 1 (C) (2016)n (D) (2016)n – 1



MATHEMATICS


SECTION - IIComprehension Type

This section contains 2 paragraphs. Based upon the first paragraph, 2 multiple choice questions and basedupon the second paragraph 3 multiple choice questions have to be answered. Each of these questions hasfour choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Question Nos. 8 to 9 Let P is a variable point on the line L = 0. Tangents are drawn to the circle x2 + y2 = 4 from P to touch it at

Q and R. The parallelogram PQSR is completed.

8. If L 2x + y – 6 = 0; then the locus of circumcentre of PQR is(A) 2x – y = 4 (B) 2x + y = 3 (C) x – 2y = 4 (D) x + 2y = 3

9. If P(3, 4) then co-ordinate of S is

(A)

2551–,

2568– (B)

2568–,

2551–

(C)

2568–,

5125– (D)

6825–,

2551–


MATHEMATICS


Paragraph for Question Nos. 10 to 12

Consider > 1 and f :

,1,1 be a bijective function such that

,1x)x(f

1)x(f 1– .

10. The value of f(1) equals(A) 2 (B) 1 (C) 3 (D) Cannot be determined

11. The value of f(f(t0)) equals where t0

,1

(A) t0 (B) 1 (C) 0t1

(D) None of these

12. Which one of the statement be true for f(x)

(A) f(x) is continuous in

,1 but not derivable (B) f(x) is continuous and derivable in

,1

(C) f(x) is discontinuous in

,1(D) None of these


MATHEMATICS


SECTION - IIIMultiple Correct Choice Type

This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONE OR MORE is/are correct.

13. Let f(x) = ax2 + bx + c ; a 0, a, b, c are integers. Let f(1) = 0, 50 < f(7) < 60 and 70 < f(8) < 80.If 13t < f(10) < 13 (t + 1) for some integer t ; then the value of t can not be.(A) 5 (B) 8 (C) 10 (D) 15

14. The value of sec4x + cosec4x + sec4x cosec4x can be(A) 18 (B) 24 (C) 32 (D) 64

15. Suppose two perpendicular tangents can be drawn from the origin to the circle x2 + y2 – 6x – 2py + 17 = 0 forsome real p, then possible value(s) of p may be.

(A) 0 (B) 5 (C) –5 (D) 15

16. Let a and c be real numbers such that c > 0 and f(x) is defined on [0, 1] as

f(x) =

0xif,0

0xif),xsin(x c–a

Which of the following statement(s) is/are correct ?

(A) f(x) is continuous if and only if a > 0. (B) f (0) exists if and only if a > 1.

(C) f (x) is continuous if and only if a > 1 + c. (D) f (0) exists if and only if a > 2 + c.


MATHEMATICS


SECTION - IVInteger Answer Type

This section contains 7 questions. The answer to each of the questions is a single-digit integer, ranging from0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. Forexample, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, thenthe correct darkening of bubbles will look like the following :In all cases round answer to nearest integer value (if required)

0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

17. If fractional part of 1x

and x2 for some x ( 2, 3 ) are equal then the value of x4 – 3x

is

18. Let lines 2x + 3y = 0 and 3x – 2y = 0 intersect at A. Let another line intersects the given two lines atB and C respectively. A circle touches AB at A and BC at D. If this circle intersects AC in E and CE = 3,CD = 6 then find length of BD.


MATHEMATICS


19. Let A(0, 1), B(1, 1), C(1, –1), D(–1, 0) be four points. If P be any other point and minimum value of

PA + PB + PC + PD = a b , where a and b are prime. Find (a + b).

20. Let L = x

1lim xln x 2x ln sinx

Find the value of 1–L


MATHEMATICS


21. Three children each accompanied by a guardian seek admission in a school. The principal want to interviewall the six persons one after the other subject to the condition that no child is interviewed before its guardian.

If number of different ways are find .10

22. Let f(x) = x 1x – 1

for all x 1.

Let f1(x) = f(x) ; f2(x) = f(f(x)) and fn(x) = f(fn–1(x)) for n >1Let P = f1(2) f2(3) f3(4) f4(5)Find the number of divisors of P.

23. Let g(y) = x y

tanx – tanylimx x1– 1– tanx.tanyy y

and f(x) = x2. If h(x) = min (f(x), g(x)), find the number of points

where h(x) is non-derivable.


PART II : PHYSICSSECTION - I


24. A transverse wave is represented by :

y =

10 sin

x2–t

T2

. Symbols have usual meaning. y, x, in cm and t, T in sec.

For what value of the wavelength the wave velocity is twice the maximum particle velocity ?(A) 40 cm (B) 10 cm (C) 60 cm (D) 20 cm

25. The position of a projectile launched from the origin at t = 0 is given by )j50i40(r m at t = 2s. If the

projectile was launched at an angle from the horizontal, then is : ( i along the ground , j vertically

upwards)(take g = 10 ms–2).

(A) tan–1 54

(B) tan–123

(C) tan–132

(D) tan–147

26. A body starts from rest on a long inclined plane of slope 45°. The coefficient of friction between the body andthe plane varies as = 0.3x, where x is distance travelled down the plane. The body will have maximumspeed (for g = 10 m/s2) when x =(A) 3.33 m (B) 12 m (C) 27 m (D) 9.8 m



PHYSICS27. In which case charge at center will experience maximum force ? (all charges are identical, regular hexagon

of side a)

(A)

Q Q

Q Q

q(B)

q q

q

q q(C)

q

qq

q

q(D)

q

q q

q

q

q

28. A man of mass 60 kg starts climbing up a massless rope by exerting 900 N on the string. After 2 sec, he isexhausted. He stops climbing and holds on to the rop.

800 kg m = 60 kg

(A) String will become slack for some time.

(B) The speed of man at the end of 2 sec. is 10 m/s

(C) Just after t = 2 sec, the acceleration of man & block will be same in magnitude

(D) The acceleration of man just after 2 sec is g/7



PHYSICS


29. A railway engine whistling at a constant frequency moves with a constant speed. It goes past a stationary

observer standing beside the rail track. The frequency (n) of the sound heard by the observer is plotted

against time (t).Which of the followings best represents the resulting curve ?

(A)

n

t

(B)

n

t

(C)

n

t

(D)

n

t

30. Different optical instruments (lens, slab) are formed using material having negative refractive index calledmeta materials. (‘n’ shows meta material) Which of the following ray diagram is INCORRECT ?

(A)

n

c

air

(B)

n

c

air

(C)

n

c

air

(D) n

c

air


PHYSICS




Paragraph for Question Nos. 31 to 32A sonometer apparatus is shown in the figure. The distance between bridges is 1 m. Linear mass density ofwire is 2 g/m. Fundamental frequency of wire is 100 Hz. When apparatus is accelerated up with accelerationa, the fundamental frequency becomes twice. [neglect length of hanging wire].

1mM

31. When sonometer apparatus is at rest, if block is made to move as a conical pendulum of angle 60º (from

vertical) then fundamental frequency of sonometer wire will increase by :

(A) 82.8% (B) 41.4 % (C) 20% (D) 1.41%.

32. The value of acceleration a is :

(A) 10 m/sec2 (B) 20 m/sec2 (C) 30 m/sec2 (D) zero.


PHYSICS


Paragraph for Question Nos. 33 to 35An equilateral prism ABC (RI = µ) is palced in air with its base side BC lying horizontally along X-axis as

shown in the figure. A ray given by 3z x 10 is incident at a point P on face AB of prism.

60º(0, 0, 0) C x

y

z

P

A

B

33. Find the value of µ for which the ray grazes the faces AC.

(A) 23 (B) 3 (C)

3 32

(D) None of these

34. Find direction of the finally refracted ray if µ = 3/2.(A) at 45º to x-axis (B) parallel to z axis (C) at 30º to z-axis (D) None of these

35. Find the equation of ray coming out of prism if bottom BC is silvered for µ = 32

?

(A) z + 3 x = 10 (B) z + x = 10 (C) 3 z + x = 10 (D) None of these



PHYSICSSECTION - III

Multiple Correct Choice TypeThis section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONE OR MORE is/are correct.

36. Which of the following is/are correct(A) Black body radiation is proportional to fourth power of absolute temperature(B) Emissive power corresponding to different wavelength is different(C) If temperature is doubled in ºC then emissive power will becomes 16 times(D) If temperature is doubled (in K) then wavelength corresponding to maximum emission will be halved

37. A man of mass 60kg pushes a spring as shown. He is standing on a weighing machine.

F

Then (Take g = 10 m/s2)(A) If push given by man equal to 200N then reading of maching will be 80 kg(B) If push given by main is 200N then reading is 60 kg(C) If he pulls spring by a force 200N then reading will be 60Kg(D) If he pulls spring by 200N then reading will be 40Kg



PHYSICS38. A light ray falls on a square glass slab as shown in the diagram. The index of refraction of the glass, if total

internal reflection is to occur at the vertical face, can be :

(A) 23

(B) 2 (C) 23

(D) 25

39. The extension produced in a wire of length L when under tension T is . One of the notes emitted by the wirewhen it is used in sonometer is (d = density, Y = Young’s modulus, mass per unit length = µ, area = A)

(A) f = 3/22 Y

d3L

(B) f = 3/22 Y

dL

(C) f = 1 AY

2L Lµ

(D) f = 1 AY

4L µL



PHYSICSSECTION - IV

Integer Answer TypeThis section contains 7 questions. The answer to each of the questions is a single-digit integer, ranging from0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. Forexample, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, thenthe correct darkening of bubbles will look like the following :In all cases round answer to nearest integer value (if required)

0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

40. The equation of state for a gas is given by PV = nRT + V, where n is the number of moles and is a positiveconstant. The initial temperature and pressure of one mole of the gas contained in a cylinder are T0 and P0

respectively. The work done by the gas when its temperature doubles isobarically is 0 0

0

P T Rx7 P

. Find x



PHYSICS41. A concave mirror of focal length 20cm and a plane mirror are kept as shown in the fig. Consider two reflec-

tions, first from concave mirror and second from plane mirror. If the image for an object kept at 30cm from

concave mirror is formed at I then the value of x is 60 3 cm.n

Find n

30cmO60º

xI

p

42. A simple pendulum bob is suspended with the help of a string of length . If at its equilibrium position, bob

is imparted a velocity v = g3 , then the angle with vertical at which the pendulum bob will discontinue the

loop is tan–1 )2x( 0 . Find x0


43. A particle is given a constant power P = 3 watt. As it moves, two resistive force F1 = K1v3 , and F2 = K2v

startsacting on it (given K1 = 1, K2 =2, v is velocity, all in SI units). The maximum velocity it acquires isV (m/s). Find V

44 Two blocks each of mass m lie on a smooth table. They are attached to two other masses as shown in thefigure. The pulleys and strings are light. An object O is kept at rest on the table. The sides AB & CD of the twoblocks are made reflecting. The acceleration of two images formed in those two reflecting surfaces w.r.t.

each other is 17g

x

m/s2. Find the value of x

m O mCA

3m 2m

B D


PHYSICS


45. A process 1 2 using 1 mole of diatomic gas is shown on the P-V diagram below. P2 = 2P1 , V2 = 4V1 . Themolar heat capacity of the gas in this process is (22R/x). Find x

P

V

2

1

46. An air column is closed in a tube sealed at one end by a Hg column having length 8cm. When the tube isplaced with its open end downward the height of air column is 20cm. If the tube is turned so that its open endis the top, the height of air column is 16cm. It the atmospheric pressure is (80 -x) cm of Hg. Find x


PHYSICS


PART III : CHEMISTRYSECTION - I


47. Select correct order of N – N bond length(A) N2 < N2O < N2O4 < N2O3 (B) N2 < N2O < N2O3 < N2O4(C) N2O < N2 < N2O3 < N2O4 (D) N2O < N2 < N2O4 < N2O3

48. Which compound can react with Na metal.(A) CH3 – CH3 (B) CH2 = CH2 (C) HC CH (D) CH3 – O – CH3

49. For the first order parallel reactions, starting with 1M of A which of the following statement is correct ?

A k3 B ; A k2 2C ; A k 3D(A) [B]t : [C]t : [D]t is dependent of time. (B) If k = 0.5 min–1, then [B] = 1M after 1.386 min(C) [C] = 0.4 M (D) [C]t > [B]t = [D]t

50.

HBrCCl4

HBrR O2 2

(A)

(B)CH CH CH=CH23 2

Hg(OAc)2

B2HH O /OH

6

2 2

(C)

(D)

NaBH4CH CH C CH3 2

Relation between A and B, C and D are :(A) Position, chain (B) Position, Functional(C) Chain, Identical (D) Metamer, Functional



51. The compound, that has lowest thermal stability(A) Na2CO3 (B) CaCO3 (C) Ag2CO3 (D) PbCO3

52. Correct set of electron defficient species is(i) BeCl2(s) (ii) AlCl3(s) (iii) BeH2(s) (iv) AlH3(s)(A) i, ii, iii, iv (B) only ii, iii, iv (C) only iii, iv (D) only (iii)

53. (I) (II) (III) (IV)

Which of the reactant is optically inactive product formed after reductive ozonolysis.(A) I (B) II (C) III (D) IV

CHEMISTRY



CHEMISTRY




Paragraph for Question Nos. 54 to 55The most common electronegative atoms in organic molecules are oxygen and nitrogen. Organic molecules

containing O – H & N – H groups show H-bond, their physical properties are chiefly due to O – H and N – H

groups. The nature of alkyl & aryl groups simply modify these properties54. Select correct order of solubility in water

(A) (C2H5)3N < (C2H5)2NH < C2H5NH2 (B) (C2H5)2NH < (C2H5)3N < C2H5NH2

(C) (C2H5)2NH < C2H5NH2 < (C2H5)3N (D) (C2H5)3N < CH3CH2NHCH3 < (C2H5)2NH

55. Select correct order(s) of boiling point which is/are explained by H-bonding(i) CH3OH < C2H5OH < C3H7OH (ii) 1º > 2º > 3º : Isomeric alcohols(iii) CH3NH2 < C2H5NH2 < C3H7NH2 (iv) 1º > 2º > 3º : Isomeric amines(A) i, ii, iii, iv (B) only ii, iii, iv (C) only ii, iv (D) only iv


CHEMISTRY


Paragraph for Question Nos. 56 to 58Two or more compounds can have many relations with each other i.e. enantiomers, diastereomers, Identical,homologues, others etc. For stereoisomers connectivity in skelaton should be same and they must be nonsuperimposable to each other

56. Which of the following are geometrical isomers and also diastereomer with each other.

(A) &

CO H2

HHOH C2

D(B) &

(C) & ClCl (D) &

57. The molecule shown are

and

(A) Constitutional isomers (B) Enantiomers(C) Diastereomer (D) Identicle

58. 3HC CH Fe

hotred (A) 3AlCl

COCl3CH (B) Cº252H/Ni C + D

relation between C and D.(A) Identical (B) enantiomer (C) diastereomer (D) position


CHEMISTRY




59. Which of the compound is having higher enol content.

(A)

O

O

(B)

O

(C)

O

(D)

O

O

60. Given A B

A

B100

200Energy(kJ mol )–1

50

Reactioncoordinate

reaction path in absence of catalyst

Which is/are correct statement ?(A) H of reaction is 50 kJ mol–1

.(B) Ea(b) is 100 kJ mol–1 in absence of catalyst(C) In presence of positive catalyst Ea(f) is 130 kJ mol–1 if it reduce threshold energy to 180 kJ mol–1.(D) In presence of positive catalyst H is less than 50 kJ mol–1.


CHEMISTRY


61. In which molecule(s), energy level of MO >MO for same value of n (principal quantum number).(A) B2 (B) C2 (C) N2 (D) O2

62. A gas obeys P(Vm – b) = RT, then which of the following statement(s) is/are correct for this gas ?

(A) Isochoric curves have slope = m

R(V – b)

(B) Isobaric curves have slope PR

and intercept b

(C) For the gas compressibility factor = 1 + b

RT(D) The attraction forces dominate over repulsive forces



CHEMISTRYSECTION - IV


0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

63. Find out total number of divalent oxygen atom(s) present in repeating unit of given pattern of double chainsilicate.

64. 23490 Th disintegrate to give 206

82 Pb as final product. Calculate difference between &



CHEMISTRY65. Maximum number of rings in solid orthoboric acid contains .................. atoms.

66. A sample of rock contains equal number of atoms of U238 and Pb206.

If age of rock is T years. Calculate the value of 9105.4T

. Given t0.5 of U238 = 4.5 ×109 years.

67. First order reaction : 2A B + C.The optical rotation per unit concentration of A, B and C are 10º, 20º and –40º respectively. The observedrotation of reaction mixture after 10 min was 20º and after completion of reaction, it was –40º. Calculate Z.Where Z = 100 k. k = rate constant for disappearance of A.[Given : ln 2 = 0.7 ; ln 3 = 1.1]



CHEMISTRY68. Number of allene possible of C3H2F2 (Including stereo)

69. For reversible raction

Given : A Bkf

kb

kb = 10–2 sec–1. Equilibrium constant K = 9Calculate time when half of equilibrium amount of B formed.


B. Question paper format :9. The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each

part has 4 sections.

10. Section I contains 7 multiple choice questions. Each question has 4 choices (A),(B), (C) and (D) for its answer, out of which only one is correct.

11. Section II contains 2 paragraphs. Based upon the first paragraph, 2 multiple choicequestions and based upon the second paragraph 3 multiple choice questions have tobe answered. Each of these questions has four choices (A), (B), (C) and (D), out ofwhich only one of correct.

12. Section III contains 4 multiple choice questions. Each question has 4 choices(A), (B), (C) and (D) for its answer, out of which one or more is/are correct.

13. Section IV contains 7 questions. The answer to each of the questions is aninteger, ranging from 0 to 9. The answer will have to be appropriately bubbled in theORS as per the instructions given at the beginning of the section.

C. Marking Scheme :

14. For each question in Section-I, you will be awarded 3 marks if you have darkenedonly the bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. In all other cases, minus one (–1) mark will be awarded.

15. For each question in Section-II, you will be awarded 3 marks if you have darkenonly the bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. In all other cases, minus one (–1) mark will be awarded.

16. For each question in Section-III, you will be awarded 4 marks if you have darkenonly the bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. No negative marks will be awarded in this Section.

17. For each question in Section-IV, you will be awarded 4 marks if you darken thebubble corresponding to the correct answer and zero mark if no bubbles is darkened.No negative marks will be awarded for in this Section.


CODE - ADATE : 10-05-15




















CODE - A


DATE : 10-05-15




1. If f(x) = ex cos (ex), x

lim f(x) = 0 and y = f

1x1x

then dxdy

at x = 1 is

(A) 21

sin 1 (B) sin 1 (C) e sin 1 (D) 2

1sine

2. Let f(x) = nLim x(x + 1) (x2 – 1)2 (cos2x)n , then f(x) is discontinuous at :

(A) all integers (B) all integers except one integer

(C) all integers except two integers (D) all integers except three integers

3. If dx)5x4x(

1x22

= f(x) + g(x) + c where f(0) = 10

3, g (–1) =

8

and c is any arbitrary constant, then the

value of f(1) + )2–3(g is -

(A) 65

1 (B)

651– (C)

6–

51–

(D) 6

–51



MATHEMATICS

4. Le f(x) =

0x0

0xx

x3tanx4tanx7tan2

Then the value of f(0) is(A) 14 (B) 0 (C) 84 (D) –84

5. dx

xsin)1x(tan1

2= f(x) + c

Where f(/2) = 0 then the value of f(/4) is(A) 1 – n 2 (B) n 2 – 1 (C) 1 + n 2 (D) –1 – n 2

6. The value of

422 is (where [.] denotes greatest integer function)

(A) 135 (B) 136 (C) 134 (D) 137



MATHEMATICS7. The number of words formed by using all the letters of the word CONICSECTION such that each word start

with consonant is(A) 965 × 7! (B) 1050 × 7! (C) 665 × 8! (D) 1155 × 7!

8. The value of 0x

Lim

(sin–1 [sin x] + cos–1 [cosx] – 2tan–1 [tan x]) is equal to

[Note : [k] denotes largest integer function less than or equal to k.]

(A) (B)2

(C)2

3(D) non-existent



MATHEMATICS


SECTION - IIMultiple Correct Choice Type


9. Let f(x) = ax4 + bx3 + cx2 + dx + e is an odd function such that f'''(0) = 6 and f'(0) = 1, then(A) Degree of f(f(x)) is 9(B) f(x) is a one-one function

(C) f(1) + f(2) + ..... + f(n) = 4

)1n(n (n2 + n + 2) (n N)

(D) f(1) + f(2) + ..... + f(n) = 0 (n N)

10. Let f(x) is differentiable x R, satisfy f(x + y) + f(x – y) = 2 f(x) x, y R, f(0) = 0, then(A) f must be odd (B) f must be even (C) f '(1) = f '(2) (D) f '(2) = f '(3) = f '(4)

11. Let us consider a function }x{b}x{a)x(f 2 (where {x} denotes fractional part of x), then

(A) If a > 0 > b and |b| > |a|, then domain of f(x) is I.(B) If a < 0 < b and |b| > |a|, then domain of f(x) is R.(C) If a > 0 and b > 0, then domain of f(x) is R.(D) If a < 0 and b < 0, then domain of f(x) is I.(I denote set of integers, R denote set of real numbers)

12. The sum of first n terms in an A.P. is 153 and the common difference is 2. If the first term is an integer andn > 2, then the number of terms in A.P. can be(A) 6 (B) 9 (C) 17 (D) 51


MATHEMATICS


SECTION - IIIMatrix - Match Type

This section contains 2 questions. Each question contains statements given in two columns, which have tobe matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II arelabelled P, Q, R, S and T. Any given statement in Column I can have correct matching with ONE OR MOREstatement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions haveto be darkened as illustrated in the following example :

If the correct matches are A – Q, S and T; B – Q and R; C – P and Q; and D – S and T; then the correctdarkening of bubbles will look like the following.

P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

13. Given the system of equations

x + y – z = 2

2x – y + 4z = 1

x + y + z =

Where , {0, 1, 2, 3, 4}, then

Column I Column II

(A) The number of ordered pairs (, ) such that the system has unique solution is (P) 1

(B) The number of ordered pairs (, ) such that the system has no solution is (Q) 4

(C) The number of ordered pairs (, ) such that the system has infinitely many soluion is (R) 20

(D) The number of ordered pairs (, ) such that the system has is consistent (S) 21

(T) 24


MATHEMATICS


14. Column I Column II(A) If 2a sinx – a sin 3x 6 x R, then number of integral values of a is (P) 3(B) For a > 0, let f : [–4a, 4a] R be an even function such that (Q) 2

f(x) = f(4a – x) x [2a, 4a] and 4h

)a2(f–)ha2(flim0h

,

then h2

)a2(–f–)a2–h(flim0h

(C) Let f be a differentiable funciton such that f '(2) = 41

, (R) 4

then

4

44

0h h)h5–2(f–)h32(f2lim

(D) If 61

nx)x.....xx1ln(lim

n2

0x

, then n = (S) 6

(T) 5



MATHEMATICSSECTION - IV


0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

15. Sum of all solutions of the equation xcos|xsin|21

, where x [0, 4] is k, then the value of k is

16. If the equation x4 – (3m + 2)x2 + m2 = 0 (m > 0) has four real solutions which are in A.P. then find the valueof 'm'.



MATHEMATICS

17. Let f(x) be a quadratic polynomial such that f(–) = f() = 0 and .4

32

f2

If ,m)x(sineccos.xsincos).x(fLimx

then find the value of m.

18. Let l = 22n )1n(n)2n)(1n(n.......432321Lim

and m = 23n )2n(n)3n)(2n)(1n(n.......54324321Lim

, then find the value of (l–1 + m–1).


MATHEMATICS


19. Let f(x) = [sec {x}] where [x] and {x} denote greatest integer and fractional part of x respectively andg(x) = 2x2 – 3x (K + 1) + K(3K + 1). Find number of integral values of K if g(f(x)) < 0 x R.

20. If obtuse angle between the normals to circle x2 + y2 – 6x – 10y + 33 = 0 which are tangents to x2 + y2 = 9

is

bacot 1– where |a| and |b| are coprime, then b + a is equal to




21. Two iron bullets at same temperature, each of mass 20g, collide head-on with each other perfectly inelastically.They were both moving at 500 m/s towards each other. If specific heat of iron is 0.1 cal/g-ºC, there rise intemperature will be closest to(A) 202º C (B) 350º C (C) 300º C (D) 410º C

22. An object is placed 1cm above the optical axis of a convex lens of focal length 40cm. The object distance is60cm. If the object now starts moving perpendicularly away from the optical axis with a speed = 10 cm/s, thespeed of the image is(A) 5cm/s (B) 10 cm/s (C) 20 cm/s (D) 40 cm/s

23. A source of frequency f gives 5 beats/s when sounded with a source of frequency 200Hz. The secondharmonic of same source gives 10 beats/s when sounded with a source of frequency 420 Hz. The value of fis:(A) 200 Hz (B) 210 Hz (C) 205 Hz (D) 195 Hz

24. A particle is hurled into air from a point on the horizontal ground at an angle with the vertical. If the air exertsa resistive force proportional to the speed of the projectile(A) the path of the projectile will be symmetrical about the vertical line through its highest position(B) At the highest point, the velocity is horizontal(C) The time for ascent equal the time for descent(D) the total energy of the projectile is conserved



PHYSICS25. A charge q is placed at the centroid of an equilateral triangle. Three equal charge 3Q are placed at the

vertices of the triangle. The system of four charges will be in equilibrium if q is equal to:

(A) –Q/ 3 (B) Q/3 (C) Q 3 (D) None

26. A carnot refrigeration cycle abosrbs heat at 270 K and rejects heat at 300K. If the cycle is abosrbing 1260 kJ/min at 270K, then work required per second is :(A) 2.33 kJ/sec (B) 4.66 kJ/sec (C) 1 kJ/sec (D) 4 kJ/sec

27. A body of mass m moving with velocity V makes a head-on elastic collsion with another body of mass 2mwhich is initially at rest. The ratio of kinetic energies of lighter body before and after collision will be-(A) 9 : 1 (B) 1 : 1 (C) 4 : 1 (D) 2 : 1

28. Coherent light consisting of two wavelengths 1 = 4500 Å & 2 = 6000 Å is sent through both slits of a Young'sdouble slit apparatus(A) Central maxima for both wavelengths will not coincide(B) The third order bright fringe of 1 will coincide with the fourth order bright fringe of 2

(C) The third order bright fringe of 2 will coincide with fourth order bright fringe of 1

(D) The fringes of wavelength 1 will be wider than the fringes of wavelength 2



PHYSICS




29. Two points on string are being observed as a travelling wave passes them. The point are at x1 = 0 and x2 = 1,the transverse motions of two points are found to be as follows

y1 = A sin (3t) and y2 = A sin 3 t8

t is in seconds and y in metre. Mark correct options(A) Frequency of wave is 3Hz (B) Frequency of wave is 1.5 Hz

(C) Wavelength may be 16m (D) Wavelength may be 16 m15

30. Rate of cooling of a body by radiation depends on(A) Area of the body (B) Mass of the body(C) Specific heat (D) Temperature of the body and the surrounding


PHYSICS


31. A ball is projected with initial speed V at distance 20cm from pole of a concave mirror. Speed of image cannotbe

f=30cm

30ºV

20cm

(A) Greater than V (B) Less than V (C) Equal to V (D) Zero

32. The lens (thin) shown here is surrounded by different media on both sides. Radii of curvature of both thesurfaces are equal

µ µ' µ"

Lens

Beam 1 Beam 2

(A) Focal length of the lens is independent of µ' for both the beams(B) If the lens is converging for beam 1 it will also be converging for beam 2(C) If µ > µ", lens is converging for beam 2(D) if µ µ", lens is converging for beam 1


PHYSICS





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

33. Young’s double slit experimental arrangement is shown in the diagram. ‘’ represents angular position ofpoint on the screen. Also, not that two slabs made up of material of refractive indices n1 and n2 and each ofthickness t = 0.2 mm are placed in front of the slits.

t

tn2

n1

Slab 1

Slab 2

O

y

x

Match the following. Column I lists values of different parameters shown n diagram. Column II lists variouspossibilities.

Column-I Column-II(A) Central maxima must be above point O (P) If = 30º and n1 = n2(B) Central maxima must be below point O (Q) If = 30º and n1 > n2

(C) Central maxima may or must be at origin O (R) If = 30º and n1 =1.3, n2 = 1.5(D) Central maxima may be below point O (S) If = 0º and n1 = n2

(T) = 0º and n1 < n2


PHYSICS


34. Column-I Column-II

(A) A particle is moving in a circle (P) The acceleration may be perpendicular to its velocity

(B) A particle is moving in a straight line (Q) The acceleration may be in the direction of velocity.

(C) A particle is undergoing projectile motion (R) The acceleration may make some angle

with angle of projection to the horizontal, (0< /2) with velocity

0 < /2

(D) A particle is moving in space (S) The acceleration may be opposite to its velocity

(T) The acceleration may be zero

SECTION - IV


PHYSICS



0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

35. A system consists of two identical cubes, each of mass 3kg, linked together by a compressed weightlessspring of force constant 1000 N/m. The cubes are also connected by a thread which is burnt at a certainmoment. At what minimum value of initial compression x0 (in cm) of the spring will the lower cube bounce upafter the thread is burnt through ?

3kg

3kg

k = 1000 N/m



PHYSICS36. There is a composite wire of aluminium and steel having uniform cross-section (A) throught. The composite

wire is in stretched condition with tension T.

1 2

steelAl

1 = 23 m, 2 = 1m.

density of Al = 2.6 gm/cm3

density of steel = 7.8 gm/cm3

the external source is of lowest possible frequency to strike resonance in the composite wire with junction asa node. How many loops on the string are formed ?

37. A particle moves on parabolic path whose equation is given by y = 2x2 with a constant speed of 2m/s.If the direction of instantaneous velocity, when it is at (2m, 4m), from the x-axis is tan–1x. Find x



PHYSICS38. One mole of an ideal gas (mono-atomic) at temperature T0 expands slowly according to law P = C T

(c is constant). If final temperature is 2T0. heat supplied to gas is 14x

RT0 . Find x

39. A convex lens of focal length 1.5m is placed in a system of coordinate axis such that its optical center is atorigin and principal axis coinciding with the x-axis. An object and a plane mirror are arranged on the principalaxis as shown in figure. Find the value of d(in m) so that y-coordinate of image (after one refraction throughlens and one reflection) is 0.3m. (take tan = 0.3)

d2m

(–2m,0.1m)0.1m

(0,0)X



PHYSICS40. A sound source S emitting a sound of frequency 500 Hz and receiver R of mass 'm' are at the same point. R

is performing SHM with the help of a spring of force constant k. At a time t = 0, R is at mean position andmoving toward right as shown in figure. At the same time, source starts moving away from the R with an

acceleration 754

m/s2. Given that 2m 100k

and amplitude of oscillation of R =

150

m, speed of

sound = 300 m/s. If the frequency (in Hz) registered by detector at t=10 second is (50x)Hz, find x.

S mR K

y

x754 m/s2




41. Hardness of water is 400 ppm. The normality and molarity of CaCO3 in the water is(A) 4 × 10–6 N, 4 × 10–6 M (B) 2 × 10–3M, 4 × 10–3N(C) 4 × 10–3 M, 8 × 10–3N (D) 4 × 10–2 M, 2 × 10–2 N

42. The correct stability order for the following species is

O

(I)

(II)O

(III)

(IV)

(A) II > IV > I > III (B) I > II > III > IV (C) II > I > IV > III (D) I > III > II > IV

43. The CORECT order of boiling point is(A) n-pentane < neo-pentane (B) p-nitrophenol < o-nitrophenol(C) NH3 < HF < H2O < H2O2 (D) H3PO4 < H3PO3 < H3PO2

44. A first order reaction 75% completed in 120 min at 300 K temperature and in 40 min at 320 K temperature.Which is incorrect statement ? (ln 3 = 1.1)(A) Half life period of reaction is 60 min at 300 K temperature.(B) 87.5% of reaction completed in 60 min at 320 K temperature.(C) Activation energy of reaction is 5.28 Kcal mol–1.(D) 87.5% of reaction completed in 180 min at 300 K temperature.



CHEMISTRY

45.HBrCCl4

A + B

Product can show which type of Isomerism(A) Position (B) Geometrical (C) Optical (D) Identical

46. The INCORRECT order is(A) Covalent character : AgCl > NaCl > KCl(B) Interaction between benzene and CCl4 : London dispersion forces(C) Order of vapour pressure : H2O > H2S > H2Se > H2Te(D) Order of boiling point in amines : RNH2 > R2NH > R3N

47. There are n container having volume V, 2V ........ nV. A fixed mass of a gas is filled in all containers connectedwith stopcock. All containers are at the same temperature if pressure of first container is P then final pressurewhen all stopcocks are opened is :

(A) )1n(nnP (B) )1n(n

nP2 (C) )1n(n

nP3 (D) )1n(n2

nP

48. Select the INCORRECT statement

(A) 1aK of fumaric acid is lower than maleic acid but reverse is true for their

2aK

(B) Hybridization of both sulphur in pyrosulphurous acid is same but oxidation state of both sulphur aredifferent(C) The N–N bond energy in N2O4 is more than N–N bond energy in N2O3

(D) The cause of solubility of inert gases in water is ion induced dipole interactions



CHEMISTRYSECTION - II


49.Br2CCl4

Identify product

(A) Br Br

(B) Br Br

(C) Br

Br(D)

Br

Br

50. Identify which are configurational (optical or geometrical) isomer.

(A) & (B) &

(C)

Br

Br Br Br (D) &

Br Br Br Br



CHEMISTRY


51. Which reaction give racemic mixture as product

(A) dil. KMnO4 (B)

dil. KMnO4

(C) dil. KMnO4

CH3 Et(D)

dil.KMnO4

CH3

Et

52. Which of the compound will show both optical isomerism and geometrical isomerism.

(A)

O O

(B)

Br Br

(C) Br Br

HH(D)

O O CH3

H


CHEMISTRY





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T


(A) SO3 (P) Polar with p-d bonds and identical S-O bond lengths

(B) OSF4 (Q) One lone pair at central atom and one p-d bond

(C) SO2 (R) Non polar with p-p & p-d bonds & identical S-O bond length

(D) ClOF3 (S) Polar with p-d bond

(T) Hybridisation of central atom is same as that in ClO2F3


CHEMISTRY


54. Column-I (Nuclear reaction) Column-II (Type of reaction)

(A) 5626Fe + ..... Mn54

25 + ..... (P) (, p) type

(B) ..... + 42He 27

14 Si + 0n1 (Q) (, n) type

(C) nB 10

105

73Li + ..... (R) (D, ) type

(D) 4320 Ca + 4

2He 4621Sc + 1H1 (S) (n, ) type

(T) emission type reaction


CHEMISTRY




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

55. In the following nine sets select total number of set(s) in which last member has higher boiling point ascompared to first memberSet-1 : CH4, SiH4, GeH4, SnH4

Set-2 : NH3, PH3, AsH3, SbH3

Set-3 : HF, HCl, HBr, HISet-4 : Glycerol, ethylene glycol, ethyl alcoholSet-5 : N2H4, NH3, HN3

Set-6 : H2O, H2S, H2Se, H2TeSet-7 : BF3, BCl3, BBr3

Set-8 : o-dichlorobenzene, m-dichlorobenzene, p-dichlorobenzeneSet-9 : o-hydroxybenzaldehyde, m-hydroxybenzaldehyde, p-hydroxybenzladehyde


CHEMISTRY


56. For a reaction : A(g) nB(g) the rate constant is 6.93 × 10–3 sec–1. The reaction is performed atconstant pressure and temperature of 24.63 atm and 300 K, starting with 1 mol of pure 'A'. If concentration

of 'B' after 200 sec is M25.33

, then calculate the value of 'n'.

57. Consider all possible isomeric carbonyl compounds (including stereoisomers) of MW = 86. All these isomersare independently reacted with Ni/H2. (Note : Stereoisomers are also reacted separately)The total number of carbonyl compounds that give only racemic product(s) is/are.

58. A smaple of ferrous sulphate and ferrous oxalate was dissolved in dilute H2SO4(aq) solution. The complete

oxidation of reaction mixture required 60 ml of 15M

KMnO4(aq) solution. After the complete oxidation all

reaction mixture was reduced by Zn and H2SO4. On again oxidation by 5N KMnO4(aq) 60 ml solution

required. What is the mole ratio of ferrous sulphate and ferrous oxalate in sample?


CHEMISTRY


59. Calculate expresion (x + y + z) for diatomic molecules :Where x = total number of singly occupied molecular orbitals (SOMO) in O2

y = total number of singly occupied molecular orbitals (SOMO) in B2

z = total number of singly occupied molecular orbital (SOMO) in NO

60. Consider following reaction :

BaCl2 + H2SO4 BaSO4 + 2HCl

400 ml of 20.8 %

Vw

BaCl2 (aq) solution and 100 ml of 4.9%

Vw

H2SO4 (aq) solution are mixed.

If 0.045 mol of BaSO4 obtained then % yield the reaction is x. Calculate the value of 30x

.

(At. wt. Ba = 137, Cl = 35.5, S = 32, H = 1, O = 16)



CODE - A




11. Section II contains 4 multiple choice questions. Each question has 4 choices(A), (B), (C) and (D) for its answer, out of which one or more is/are correct.

12. Section III contains 2 questions. Each questions has four statements (A, B, C and D)given in Column I and five statements (P, Q, R, S and T) in Column II. Any givenstatement in Column I can have correct matching with one or more statement(s)given in Column II. For example, if for a given question, statement B matches with thestatements given in Q and R, then for that particular question, against statement B,darken the bubbles corresponding to Q and R in the ORS.


C. Marking Scheme :

14. For each question in Section I, you will be awarded 3 marks if you darken thebubble corresponding to the correct answer and zero mark if no bubble is darkened.In case of bubbling of incorrect answer, minus one (–1) mark will be awarded.

15. For each question in Section-II, you will be awarded 4 marks if you have darkenonly the bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. No negative marks will be awarded in this Section.

16. For each question in Section III, you will be awarded 2 marks for each row inwhich you have darkened the bubble(s) corresponding to the correct answer. Thus,each question in this section carries a maximum of 8 marks. There is no negativemarking for incorrect answer(s) for this section.

17. For each question in Section IV, you will be awarded 4 marks if you darkened thebubble corresponding to the correct answer, and zero mark if no bubble is darkened.There is no negative marking for incorrect answer(s) for this section.

DATE : 10-05-15




















CODE - A


DATE : 07-06-15




1. The maximum value of 2xcos

2xsinxcos3xsin4 22 is

(A) 4 (B) 9 (C) 23 (D) 24

2. The complete set of the values of a for which both roots of the equation x2 – ax + 2 = 0 belongs to [0, 3]

(A) 311a22 (B) 11a22 (C) 22–a (D) a 5

3. If a > b > 0; then the maximum value of xsinbxcosa

xcosxsin)b–a(ab22222

22

when

2

,0x is

(A) 2

ba 22 (B)

2ba 22

(C) a2 – b2 (D) a2 + b2




MATHEMATICS4. If Cr's denote the combinatorial co-efficient in the expansion of (1 + x)n ; then

2 nn

n n–1 n–2 0n

1 1 1lim C – C C .....(–1) C3 3 3

is

(A) 2 (B) 0 (C) 1 (D) Does not exist

5. Let 1sinx)1–a(4xsin–

4xcos)2a3–a()x(f 222

.

The largest integral value of 'a' for which f '(x) 0 x R(A) 2 (B) 1 (C) 3 (D) 4

6. The number of functions which are not ONTO; defined from set A to set B where A consists of 6 elements andB has 4 elements(A) 2530 (B) 2536 (C) 4536 (D) 4324

7.

441eccos)9(cot

813tan–tan 1–1–1– is equal to

(A) (B) 87

(C) 85

(D) 4

3



MATHEMATICS

8. If

0x,1–0x,00x,1

)x(f

and g(x) = cos (x – /4) – sin (x – /4) then points, where f(g(x)) is discontinuous in 0 x 2 are

(A) 2

3,2

(B)

47,

43

(C) 4

5,4

(D) 0, , 2

9. The value of definite integral dxxsin2

0

(A) 2

(B) 2 (C) (D) 2

10. If h1, h2 and h3 are the lengths of the altitudes of a triangle then 321 h1

h1

h1

equals to

(A) r1

(B) r2

1(C)

r2

(D) r3

(Where r is inradius of the incircle of the triangle)



MATHEMATICS

11. Degree of the polynomial 1–x21–x23x2x3–x3x31–x3x22–x1xxx

)x(f2

2

2

is

(A) 0 (B) 1 (C) 2 (D) 4

12. If the pair of lines joining the origin to the point of intersection of the curve 1by

ax

2

2

2

2 by the line

x + my + n = 0 are coincident then(A) a22 + b2m2 = n2 (B) a2m2 + b22 = n2

(C) 2222

2 mb1

a1n

(D) None of these

13. If dttnxyx

1

2 ; then the value of 3

3

dxyd

at x = e

(A) 33 (B) 11 (C) 4

33(D) None of these



MATHEMATICS

14. If f(x) is continuous function such that f(x) > 0 x 0 and (f(x))2014 = 1 + dt)t(fx

0 then the value of (f(2014))2013

is equal to(A) 2013 (B) 2014 (C) 2015 (D) 2016

15. The value of

17

1k 18ksin is

(A) 1629

(B) 1729

(C) 16211

(D) 17213

16. The number of seven digit numbers with the sum of digits equal to 10 which can be formed by using the digits1, 2, 3 only is equal to(A) 84 (B) 80 (C) 78 (D) 77

17.2

2

max(x | x |, x [x])dx

(where [x] denotes the greatest integer x) is equal to

(A) 4 (B) 5 (C) 6 (D) 8



MATHEMATICS

18. If a, b, c are the pth, qth, rth terms of an H.P., then value of determinant

bc ca abp q r1 1 1

is equal to

(A) 0 (B) abc (C) pqr (D) 2abc

19. If y is a function of x given by 2logy – logx – log(y – 1) = 0, then for y(x)(A) the domain and range are both (2, )(B) the domain is (0, ) and range is (1, )(C) the domain is [4, ) and range is (1, )(D) the domain is [4, ) and range is (2, )

20. 20x )x2cos–1(xtanx2–x2tanxlim

is

(A) 2 (B) –2 (C) 21

(D) 21

21. 2 20

xlogxdx(1 x )

(A) 0 (B) 2

(C) 4

(D) 1


MATHEMATICS


22. If 3 3sin cos

sin( 3 ) cos( 3 )

, then 22 – 1 is equal to

(A) sin (B) cos (C) 2cos (D) tan

23. Let f:R R be a differentiable function satisfying f(y) f(x – y) = f(x) x, y R and f(0) = 3, then(A) f(3) = 3 (B) f(1) = 2f(1) (C) f(3) = (f(1))3 (D) f(3) = (f(1))2

24. If nC0, nC1, nC2,.....nCn are binomial coefficient such that nCn–3, nCn–2, nCn–1 are in A.P., then n =(A) 7 (B) 14 (C) 3 (D) 5



MATHEMATICS

25.1

3 20

2 dx(x 6x 11x 6)

(A) 5ln2 – 3ln3 (B) 3ln3 – 5ln2 (C) 5ln2 + 3ln3 (D) 5ln5 – 2ln2

26. If

3r3r4r44r4tan 23

1r

1– = –

4

+ cot–1 m, then m is :

(A) – 31

(B) 31

(C) 3 (D) – 3

27. If f(x) 2xb)b–xsina(xcos

, x 0

= 2, x = 0,the values of 'a' and 'b' so that f(x) is continuous at x = 0 is(A) a = 0, b = 4 (B) a = 0, b = –4 (C) a = –1, b = 2 (D) a = 2, b = 2


28. Let f(x) = 4

x2cosx2sin , g(x) = x2 – 4. If g(f(x)) is surjective, then it is invertible for x

(A)

0,

2 (B)

,2 (C)

8,

8 (D)

2

,0

29. nlim

2/3n10n8n........321

is equal to

(A) 152

(B) 151

(C) 154

(D) 157

30.

2/

0

2

xsin2xcosxxsinx4

dx is equal to :

(A) 2

(B) 4

2(C)

4

(D) 16

2


MATHEMATICS




31. Two small spheres of mass M1 and M2 are suspended by weightless insulating threads of lengths L1 and L2.The spheres carry charge of Q1 and Q2 respectively. The spheres are suspended such that they are in levelwith one another and the threads are inclined to the vertical at angles of 1 and 2 as shown. Which one of thefollowing conditions is essential, if 1 = 2 ?

M1 M2+Q2+Q1

1

2

L1

L2

(A) M1 M2 but Q1 = Q2 (B) M1 = M2 (C) Q1 = Q2 (D) L1 = L2

32. A mixture of two moles of Hydrogen and one mole of argon gas is taken in a closed container at roomtemperature. Consider the following two statements(i) The average translational kinetic energy of each molecule of Hydrogen and Ar is same.(ii) The pressure due to argon gas is more than that due to hydrogen gas.(A) Both statement (i) and (ii) are correct(B) Statement (i) is correct while statement (ii) is incorrect(C) Both statement i) and ii) are incorrect(D) Statement (i) is incorrect while statement (ii) is correct

33. Figure shows two conducting thin concentric shells of radii r and 3r. The outer shell carries charge q andinner shell is neutral. The amount of charge which flows from inner shell to the earth after the key K is closed,is equal to :

(A) q–3

(B) q3

r

3r

q

k(C) 3q(D) –3q



PHYSICS


34. Two charges q1 and q2 are kept on x-axis and electric field at different points on x-axis is plotted against x.Choose correct statement about nature and magnitude of q1 and q2 :

xq1 q2

E

(A) q1 +ve, q2 –ve ; |q1| > |q2| (B) q1 +ve, q2 –ve ; |q1| < |q2|(C) q1 –ve, q2 +ve ; |q1| > |q2| (D) q1 –ve, q2 +ve ; |q1| < |q2|

35. If coefficient of friction between all surfaces is 0.4, then what will be the minimum force F to have equilibriumof the system (see figure).

25kg 15kg F

(A) 62.5 N (B) 150 N (C) 31.25 N (D) 50 N

36. A uniform rope of linear mass density and length is coiled on a smooth horizontal surface. One end ispulled up with constant velocity v. Then the average power applied by the external agent in pulling the entirerope just off the ground is :

(A) 2

21 gv2 2

(B) 3v21

2gv

(C) 21 vgv2 2

(D) None of these


PHYSICS


37. A source of sound with natural frequency 1.8 kHz moves uniformly along a line separated from a stationarylistener by a distance = 250 m. The velocity of source is equal to n = 0.8 fraction of the velocity of sound.What will be the frequency of sound received by the listener at the moment when the source gets closest tohim.(A) 5 × 103 Hz (B) 3 × 103 Hz (C) 8 × 103 Hz (D) None of these

38. Figure shows a snapshot of a vibrating string at t = 0. The particle P is observed moving up with velocity

20 3 cm/sec. The tangent at P makes an angle 60º with the x-axis, then which can be the equation of

wave.

(A) y = (0.4 cm) sin 2 –1 –11 1(5s )t cm x4 8

1.53.5

5.5 7.560ºP

4

(in 10 m)–3

(in 10 m)–2

y

x2 2(B) y = –1 –11 3(2 2 cm)sin2 (5s )t cm x

4 8

(C) y = (0.4 cm) sin 2 –1 –11 3(5s )t – cm x4 8

(D) None of the above

39. Figure shows N identical blocks connected with identical springs on a smooth horizontal surface. A constantforce is pulling the blocks horizontally. During motion all the springs have acquired their stable configurations.If stretch in spring connecting 4th and 5th block is two times that between 8th and 9th block what is totalnumber of blocks.

PN N – 1 2 1

(A) 6 (B) 8 (C) 10 (D) 12


PHYSICS


40. The primary purpose of using a parabolic mirror in a reflecting telescope is(A) To collect more light from a distant galaxy (B) To increase the magnification(C) To overcome diffraction effects (D) To correct for spherical aberration

41. A particle moves on a rough horizontal ground with some initial velocity say 0. If 34

th of its kinetic energy is

lost in friction in time t0. Then coefficient of friction between the particle and the ground is :

(A) 0

02gt

(B) 0

04gt

(C) 0

0

24gt

(D) 0

0gt

42. A small object hides under a floating disc of radius R, where R3 = 27 .

If the index of refraction of liquid is 2 .

Then volume of liquid in which it can be present without being seen by from any observer in air is:

(A) 9 (B) 6 (C) 3 3 (D) 12

43. In a two slit experiment with monochromatic light, fringes are obtained on a screen placed at some distancefrom the slits. If the screen is moved by 5 × 10–2 m towards the slits, the change in fringe width is 3 × 10–5

m. If the separation between the slits is 10–3 m, the wavelength of light used is :(A) 6000 Å (B) 5000 Å (C) 3000 Å (D) 4500 Å


PHYSICS


44. In a compound microscope, the final image formed at a distance ‘d’ from the eyepiece, whose focal length isfe, where d > D = LDDV (least distance of distinct vision). The object is placed at a distance ‘u’ from theobject lens, whose focal length is f0. The angular magnification of the microscope is :

(A) 0

0 e

f D 1u – f d f

(B) 0

0 e

Df 1 1u – f d f

(C)

0

0 e

Df 1 1u – f d f

(D) 0

0 e

Df 1 1u f d f

45. Consider a block moving in a horizontal circular path on the inner surface of a cone. The normal force on theblock is.

(A) mg (B) always greater than mg(C) may be greater or less than mg (D) always less than mg

46. In a heat insulated vessel there is a tap water of 15ºC. We place in it 'n' ice cubes of –15ºC taken out of the

deep freezer. Specific heat of ice = specific heat water

2. Each ice cube has same mass as mass of water

in vessel, then(1) If n = 1, some ice will melt (2) If n = 1, some water will freeze(3) If n = 2 some water will freeze (4) If n = 2, final temp is 0ºC(A) 1 & 2 are correct (B) 1, 4 are correct (C) 1 & 3 are correct (D) 2 & 4 are correct

47. A plane wave of monochromatic light falls normally on a uniformly thin film of oil which covers a glass plate.The wavelength of source can be varied continuously. Complete constructive interference is observed inreflected light for 1 = 5000 Å and 1 = 10000 Å and for no other wavelength in between. If µ of oil is 1.25 andthat of glass is 1.5, the thickness of film will be ........ µm.(A) 0.2 (B) 0.1 (C) 0.4 (D) None of these


PHYSICS


48. What is the amount of work required to be done to increase the temperature of one mole of an ideal gas by30ºC, if it is expanding under the condition P V2/3 .(A) 150J (B) 100J (C) 50J (D) 200J

49. Which of the following statements is not true about reference frames(A) In a non inertial reference frame an isolated particle does not retain a constant velocity(B) A reference frame travelling with acceleration relative to an inertial frame is a non-inertial frame(C) In an inertial frame, velocity vector of an isolated particle changes neither in direction nor in magnitude(D) If a block is stationary in an elevator then reference frame fixed to elevator must be inertial

50. A ball is thrown vertically up in air where the resistive force can be considered to be constant. If time of ascentis t1 and time of descent is t2. The ratio of velocity of projection to the velocity just before it hits the ground is

(A) 2

1

tt (B)

22

1

tt

(C) 2

1

2tt (D)

2

1

t2t

51. Figure shows three spherical and equipotential surfaces 1,2 and 3 round a point charge q. The potentialdifference V1 – V2 = V2–V3. If t1 and t2 be the separation between them. Then

q t1

t2

1

23

(A) t1 = t2 (B) t1 > t2 (C) t1 < t2 (D) t1 t2


PHYSICS


52. In an experiment to estimate the distance of a black board from a student using parallax method, 10 markingsare made separated by 10.0cm from each as shown in the figure below. The student holds a pen in the handin front of the eyes in the direction of the board. When she sees the pen with only left eye, it coincides with8th marking on the board. When she sees the pen only with right eye, then the pen appears to coincide with2nd marking. If the separation between eyes for normal human being is 8.0 cm and pen to eye distance is30.0 cm, then distance from the student to the board is

(A) 225 cm (B) 145cm (C) 255 cm (D) 175 cm

53. One mole of an ideal gas is taken along the process in which PVx = constant. The graph shown representsthe variation of molar heat capacity of such a gas with respect to 'x'. The values of c' and x' respectively, aregiven by

(A) 5 5R,2 2

(B) 5 5R,2 3 x

x'O

(3/2)R

c'C

(C) 7 7R,2 2

(D) 5 7R,2 5


PHYSICS


54. Two bodies of equal masses are heated at a uniform rate under identical conditions. The change in temperature

in the two cases is shown graphically, then the ratio of their latent heats 1

2

LL and specific heats

1

2

CC will be

(A) 1 1

2 2

L C1 & 3L 2 C

(B) 1 1

2 2

L C 12 &L C 3

I

IIx

0 2 4 6 7

4060

Temp (ºC)

time(min.)

(C) 1 1

2 2

L C4 & 3

L C

(D) None of the above

55. A particle of mass m moving with velocity u makes an elastic one-dimensional collision with stationaryparticle of mass m.

F0

T/2 T

F

They are in contact for a very brief time T. Their force of interaction is plotted in the figure shown. Then themagnitude of F0 is

(A) muT

(B) 2mu

T(C)

mu2T

(D) none of these



PHYSICS56. An optical system produces an image of an object as shown in the figure below. Guess the optical system

and its position.

h

obiect

1.2 h

image

Optic axis

(i) concave mirror between the object and the image(ii) Biconvex lens on the left of the object.(iii) convex mirror between the object and the image(A) (i), (ii) and (iii) are possible (B) only (ii) and (iii) are possible(C) only (i) and (iii) are possible (D) only (i) and (ii) are possible

57. The angle of a prism is 60º. When light is incident at an angle of 60º on the prism, the angle of emergence is40º. The angle of incidence i for which the light ray will deviate the least is such that

(A) i < 40º (B) 40º < i < 50º (C) 50º < i < 60º (D) i > 60º

58. The intensity ratio of the two interfering beams of light is .

What is the value of max min

max min

I I

I I ?

(A) 2 (B) 21

(C) 2

1 (D) 12


59. A lift of total mass M is raised by cables from rest to rest through a height h. The greatest tension which thecables can safely bear is nMg. The maximum speed of lift during its journey if the ascent is to be made inshortest time is

(A) n 12gh

n

(B) 2ghn (C) n2gh

n 1

(D) n 12gh

n

60. Velocity versus displacement graph of a particle moving in a straight line is shown in figure.

10

10 S(m)

V(m/s)

Corresponding acceleration versus velocity graph will be

(A)

10

10 V(m/s)

a(m/s )2

(B)

10

10 V(m)s

a(m/s )2

(C)

10

V(m)s

a(m/s )2

(D)

10

10a(m/s )2

V(m/s)


PHYSICS




61. Which of the following catagories of salts of alkali and alkaline earth metals show same solubility trend inwater.(i) Carbonates (ii) Nitrates (iii) Hydroxides (iv) Chlorides(A) (i) and (ii) (B) (ii) and (iv) (C) (ii) and (iii) (D) Only (ii)

62. Most reactive towards SN–Ar

(A)

BrNO2

NO2

(B)

Br

NO2

NO2

(C)

Br

NO2

(D)

Br

NO2

63. A radioactive isotope ZXA is converting into Z – 8YA – 16 by -decay. If 1 g atom of ZXA, produced 3 mole of Heatom in 34.65 hour then disintegration constant of ZXA is (in hour–1)(A) 8 × 10–2 (B) 4 × 10–2 (C) 2 × 10–2 (D) 3.6 × 10–3




CHEMISTRY64. Select the INCORRECT match for given reaction.

(P)(Oxysalt)

(T < 800ºC)

(Q)(Metal oxide)

+ Other product(s)

Oxysalt(P) Metal Oxide(Q)(A) FeCO3 FeO(B) Fe2(SO4)3 Fe2O3

(C) FeC2O4 Fe2O3

(D) FeSO4 Fe2O3

65. 10 mol of SO2 gas is heated from 300 K to 400 K along different path AB, AD and AC.What is the value of Z (in kcal)? Where Z = qAB + qAD – qAC. (Given : TB = TC = TD = 400 K)

A

BD

CT = 300KA K

P

V(A) 2 (B) 3 (C) 4 (D) 5

66. HBr(1 equivalent) Major product is :

(A) Br (B) Br

(C) Br

(D) Br



CHEMISTRY67. Select the CORRECT order of basic strength

(A) BaO < NiO (B) CaO < ZnO (C) FeO < Fe2O3 (D) Na2O < K2O

68.

C

CH

OH

1. NaNH (2eq.)2

2. CH CH –3 2 II3. CH –

4. H /Pd-BaSO3

2 4

Product (X) is :

(A)

CH –O–CH2 3

CH3CH2

(B)

OCH3

CH2CH3

(C)

CH2–OCH CH2 3

CH3

(D)

O–CH CH2 3

CH3

69. What is net heat exchange (q) by 10 mol of CO2(g) in a cyclic process describe by V-T- graph as following(Given : ln 2 = 0.7).

A

B C

D

20L

10L

300K 400KT

V

(A) q = –1000 Cal (B) q = –1400 Cal (C) q = –9800 Cal (D) q = –5600 Cal


CHEMISTRY


70. Which of the following statement is NOT CORRECT forNO2 , NO2

+, NO2–

(A) NO2 is paramagnetic(B) NO2

+ is linear , NO2 is bent and bond angle is slightly less than 120º(C) NO2

+ ion has the shortest and strongest bonds among these(D) NO2

– ion has longest and weakest bond among these

71. 10 mol of an ideal gas is heated from 200 K to 400 K adiabatically reversibly. Work done by the gas is

[Given : Cv, m (Cal mol–1 K–1) = 10 + 100T

; n 2 = 0.7]

(A) 700 Cal (B) 2000 Cal (C) 2700 Cal (D) 20700 Cal

72.

CH3

(i) 3Cl /Light2

(ii) KOH(aq)(iii) PCl /5 (iv) Pd-BaSO4H /2

Product is :

(A)

CH2–OH

(B)

CHO

(C)

COOH

(D)

CH OH2

73. Which compound has the smallest bond angle in each set(I) OSF2, OSCl2, OSBr2 (Halogen – S – Halogen bond angle)(II) SbCl3, SbBr3, SbI3 (Halogen – Sb – Halogen bond Angle)(III) PI3, AsI3, SbI3 (Halogen – Central Atom – Halogen bond angle)(A) OSBr2, SbCl3, SbI3 (B) OSCl2, SbBr3, AsI3

(C) OSF2, SbCl3, SbI3 (D) OSF2, SbCl3, PI3



CHEMISTRY

74. (A)

Br /CCl2 4

Cold KMnO4

Meso 2,3-dibromobutane (X)

(Y)

Product (Y) is :(A) Racemic mixture (B) Meso (C) Diastereomers (D) Constitutional isomers

75. The third virial coefficient of a He(g) is 4 × 10–2 (litre/mol)2.What will be the volume of 5 mol of He(g) at 1 atm and 273 K?(A) 23.4 L (B) 22.6 L (C) 112.2 L (D) 113 L

76. Which of the following match is CORRECTLigand Property(A) Thiosulphato Tridentate ligand(B) Glycinato Symmetrical bidentate ligand(C) DMG (Dimethylglyoximato) Both 'O' and 'N' are donor sites of ligand(D) Nitrito Ambidentate as well as flexidentate

77. Complete oxidation of 1 mol benzene by evolution of 780 kcal of heat at 300 K at constant pressure.How much heat is released in same reaction at constant volume at 300 K ?(A) 771 kcal (B) 780.9 kcal (C) 779.1 kcal (D) 120 kcal



CHEMISTRY78. How many products are possible on monochlorination of all isomers of C5H12.

(A) 9 (B) 10 (C) 11 (D) 12

79. Which of the following combination of ions does not bring redox reaction at room temperature(A) Pb2+(aq) + 2I–(aq) (B) Sn2+(aq) + Hg2+(aq)(C) Fe3+(aq) + 3I–(aq) (D) Cu2+(aq) + 2CN–(aq)

80. Which molecule has centre of symmetry present (in any possible stable conformation) ?

(A)

COOHH OH

H OHCOOH

(B)

COOHH OH

HO HCOOH

(C)

CH3

BrH H

CH3

Br(D) O

O

O

O

81. Statement-1 : Temperature of an ideal gas may increase, decrease or remains constant in an adiabaticprocess.Statement-2 : (Cp, m / Cv, m) for an ideal gas decreases when we consider vibrational degree of freedom.(A) Only statement-1 is True. (B) Only statement 2 is True.(C) Both are correct statements. (D) Both are incorrect statement.



CHEMISTRY82. Which of the following complex species is following E.A.N. Rule

(A) [Ca(EDTA)]2– (B) [Cr(en)3]3+ (C) [CoBrCl(trien)]+ (D) [Ni(dmg)2]

83. One mole of an ideal gas (Cv,m = 32

R) at 300 K and 4 atm pressure is expanded adiabatically to a final

pressure of 2 atm against a constant pressure of 2 atm. Decrease in enthalpy of gas in process is :(A) 30 cal (B) 180 cal (C) 240 cal (D) 300 cal

84. What will be the lowest molecular mass of chiral cycloalkane (No isotopes are allowed).(A) 56 (B) 68 (C) 70 (D) 84



CHEMISTRY85. A heat engine is operating between 700 K to 500 K and it absorbs 21 kcal of heat from 700 K reservoir

reversibly per cycle. The work done by the heat engine in two cycles is(A) 4 kcal (B) 6 kcal (C) 12 kcal (D) 60 kcal

86. What are the products obtained on hydroboration-oxidation of the given alkene

CH3

(I)

CH3

HOH

(II)

CH3

HOH

(III)

CH3

HOH

(IV)

CH3

HOH

(V)

CH3

HOH

(VI)

CH3

HOH

(A) I and III (B) II and IV (C) II and VI (D) III and V

87. Correct order of C–O bond length for compounds(I) H3B.CO (II) [Fe(CO)4]2– (III) [Co(CO)4]–

(A) I > II > III (B) II > III > I (C) II > I > III (D) III > I > II



CHEMISTRY88. What is the maximum number of products possible when 2-chloro-3-phenylbutane is undergone through

hydrolysis (SN1) :(A) 2 (B) 3 (C) 4 (D) 5

89. Which of the following is organometallic compound(A) KCN (B) CaC2 (C) CH3COONa (D) [Mn(CO)2(NO)2]–

90. The density of 2.0 molal aq. solution of NaOH is 1.20 g/ml. What is the molarity of NaOH solution?(A) 1.57 M (B) 1.11 M (C) 2.4 M (D) 2.22 M




C. Marking Scheme :



CODE - ADATE : 07-06-15




















CODE - A


DATE : 28-06-15




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

1. Let ABC be the right angled isoceles triangle right angle at C whose equal sides have length 1, P is a pointon the hypotenuse, and the feet of the perpendiculars from P to the other sides are Q and R. Consider theareas of the APQ, PBR and area of quadrilateral QCRP.

The largest of these three areas is atleast ba

(a, b N and coprime)

Find |b – a|.

2. In a triangle ABC, the medians to the sides AB and AC are perpendicular.

If the minimum value of cot B + cotC equals to qp where p and q are coprime natural numbers. Find (p + q).



MATHEMATICS


3. Find the reciprocal of the limit x 0lim

x(x –1) x

2x2

e – x

x – 1

4. If f(x) + f

x1–1 = 1 + x

x R – {0, 1}Find the value of 4f(2).

5. Find the maximum value of

4x5x–13x6–x3–x 2424


MATHEMATICS


6. A variable line ax + by + c = 0. Where a, b, c are in arithmatic progression, is normal to a circle(x – )2 + (y – )2 = , which is orthogonal to the circle x2 + y2 – 4x – 4y – 1 = 0.Find the value of (+ + ).

7. For any 2 squares, the sum of whose area is 1, a rectangle of area A exists into which the squares can beplaced without over lapping of interior points (Assume that the squares are to be placed with their sides

parallel to the sides of the rectangle). The least value of A can be expressed as 1

where and are

natural numbers. Find (+ ).

8. If 2x3 – 6x + = 0 has three real and distinct roots. Find the number of distinct integral value(s) of 'a'.


MATHEMATICS




9. Let x, y and z are real numbers and x + y + z = 5 and xy + yz + zx = 3 and least and greatest value of z arem and M respectively then

(A) m = 31

(B) M = 310

(C) m = – 1 (D) M = 313

10. Consider the curve x3 + xy + y3 = 3 and line x + y = k (k R). Which of the following statement(s) is/arecorrect(A) line is tangent to the curve if k = 2 (B) line is tangent to the curve if k = 3

(C) line meets the curve in two points if 2 < k < 3 (D) line meets the curve in two point if 31

< k < 2

11. If = sin 47º + sin 61º – sin11º – sin25º then

(A) > 22

13 (B) <

415

(C) > cos 1 (D) < cos 2


MATHEMATICS


12. If ax2 + bx + c = 0 has no real roots and a + b + c < 0 then(A) 4a – 2b + c > 0 (B) 4a – 2b + c < 0 (C) 13a + 5b + 2c < 0 (D) 5b – 25a – c > 0

13. Which of the following statement(s) is/are correct for f(x) = x1/3(x – 1)

(A) has two points of inflection (B) is strictly increasing for x > 41

(C) is concave down in

0,21– (D) minimum value of f(x) is 3/44

3–

14. Let f(x) be a increasing function defined on (0, ). If f(2a2 + a + 1) > f(3a2 – 4a + 1)then the possible integral value of 'a' is/are(A) 1 (B) 2 (C) 3 (D) 4

15. Let In =

2/

0n

2

)xtanx(secxsec

dx ; n > 1 then which of the following statement is/are correct :

(A) I3 = 83

(B) I2 + I4 = 1514

(C) I3 + I5 = 125

(D) I2 + I3 = 2425


MATHEMATICS


16. The greatest value of the function f(x) = x4 – 6bx2 + b2 on the interval x [–2, 1] depends on the parameterb. Which of the following statement(s) is/are correct.(A) greatest value is b2 if b = 2015 (B) greatest value is b2 – 24b + 16 if b = 2016(C) greatest value is b2 – 24b + 16 if b = – 2016 (D) greatest value is b2 if b = – 2016

17. A tangent drawn to the curve y = x2 + 4x + 8 at P(, ) touches the curve y = x2 + 8x + 4 at Q (a, b) then(A) + a = 2 (B) + b = 24 (C) a= 2 (D) b= 8

18. If f(x) = 5)1–x(xsinBx5sinAx3sin

(x 1)

is continuous at x = 1 ; then

(A) A = – 51

(B) B = 2 (C) f(1) = 516

5 (D) f(1) = 165


MATHEMATICS





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

19. For the function f(x) = ax2 – b|x|Column-I Column-II

(A) f(x) has a local maximum at x = 0 (P) a > 0, b > 0(B) f(x) has a local minimum at x = 0 (Q) a > 0, b < 0

(C) f(x) has a local extremum at x = a2b

(R) a < 0, b < 0

(D) f(x) is not differentiable at x = 0 (S) a < 0, b > 0(T) can not determine


MATHEMATICS



(A) Let a, b are real numbers such that a + b = 1 then the (P)2

minimum value of the definite integral

0

2)x2sinbxsina( dx equals to

(B) 2/

0

2 dx21–xsinx equals (Q)

4

(C) A rectangle is inscribed in a given semicircle with one of its (R) 8

side along the diameter. If k times the area of the largestrectangle equals the area of the semicircle then the valueof k equals

(D) If L = 0xlim

xx)x(sin–)x(tan

3

2/32/3

then the value of L equals (S) 3

(T)4

3




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

21. A long thick cylinder of radius R (uniformly charged with density coulomb/m3) has a spherical cavity of

diameter R touching its axis. If electric field at centre of cavity is 0

Rn , find n.

22. A drop (part of sphere )of width 2.4 mm of some liquid (surface tension 0.03 Nm–1) is put on glass as shown.The contact angle is sin–1(0.1). Find the excess pressure inside drop in pascal.

glass

2.4 mm



PHYSICS


23. A massless spring of force constant 1000 N/m is compressed a distance of 20 cm between discs of 8 kg and2 kg. Both discs and spring are given an initial velocity 3 m/s perpendicular to length of spring as shown infigure. What is ground frame velocity of 2 kg block (in m/s) when spring regains its natural length. (Discs areplaced on smooth horizontal surface)

B8kg

2kgA

3m/s

3m/s

3m/s

24. A string 25 cm long fixed at both ends and having a mass of 2.5g is under tension of 25N. A pipe closed fromone end is 40 cm long. When the string is set vibrating in its first overtone and the air in the pipe in itsfundamental mode, beat are heard. It is observed that increasing the tension in the string decrease the beatfrequency. If the speed of sound in air is 328 m/s, find the beat frequency.

25. Three coherent sources generating waves in the same phase are placed as shown. The wave length of thewave is 40 × 10–7m. The minimum distanced (in m), such that intensity at point D is 9 times the intensityof each source will be _________.

d d d

S1 S2 S3D


PHYSICS


26. The velocity distribution in a viscous flow over a plate is given by u = 4y – y2 for y 2m where u = velocityin m/s at a point distant y from the plate. If the coefficient of dynamic viscosity is 1.5 in SI units, determinethe shear stress at y = 0 in N/m2.

27. In the diagram shown, the lens is moving towards the object with a velocity 2 m/s and the object is alsomoving towards the lens with the same speed. What is speed of the image with respect to earth when theobject is at a distance 2f form the lens? (f is the focal length) :

V

V

Object

28. A steel rod is 4 cm in diameter at 30°C. A brass ring has an interior diameter of 3.992 cm at 30°C. In orderthat the ring just slides onto of the steel rod, if the common temperature of the two is 40N (in °C), find N(steel = 11 × 10–6/°C , brass = 19 × 10–6/°C )


PHYSICS




29. A small dipole p

is placed inside an irregular cavity of a spherical conductor having a charge Q on it. Choose

the INCORRECT option(s)(A) Net force on dipole is zero(B) The charge on outer surface of conductor is non uniform(C) The electric field at a distance r from the dipole in its line outside conductor due to charge on outer

surface of conduction is 32KPr

(D) Net force on sphere is zero

30. In YDSE the lower slit is covered by a thin glass sheet. Which of the following option(s) may restore centralmaximum at perpendicular bisector of original slits ?(A) Turning incident rays anitclockwise(B) Displacing upper slit up a little(C) Using a thin prism in between plane of slit & screen(D) Using a converging lens in between plane of slit & screen with bisector of slit as its optical axis

31. Which of the following is correct statement(A) The fraction of volume submerged of any floating body is any liquid is equal to its relative density w.r.t.water(B) If a floating body absorbs some water the fraction of volume submerged will increase(C) If only liquid expands due to heating the fraction of volume submerged of a body decreases(D) If only floating body expands due to heating the fraction of volume submerged of the body decreases


PHYSICS


32. A beam of white light is incident on a combinations of thin prisms with equal angles. In the out going beamthe rainbow colours are observed as shown. stands for refractive index and for angle of dispersion. Then

RY

V

Whitelight

2

1

(A) 1 < 2 (B) 2 = 1 (C) 1 > 2 (D) 1 > 2

33. Which of the following functions of x and t represens a progressive wave

(A) y = sin(4t – 3x) (B) 21y

4 (4t 3x)

(C) 1y

4t 3x

(D) None

34. S is a solid neutral conducting sphere. A point charge q = 1 x 106 C is placed at point A. C is the centre ofsphere and AB is a tangent, BC = 3 m and AB = 4m.(A) The electric potential at C due to induced charges on the sphere is 0 V.

A B

CS

(B) The electric potential at C due to induced charges on the sphere is 1.2 kV.(C) The electric potential at B due to induced charges on the sphere is 0.45 kV.(D) The electric potential at B due to induced charges on the sphere is 0.45 kV.



PHYSICS35. For two different gases X and Y, having degrees of freedon f1 and f2 and molar heat capacities at constant

volume 1VC and

2VC respectively, the n P versus n V graph is plotted for adiabatic process, as shown

n P

n V

xy

(A) f1 > f2 (B) f2 > f1 (C) 12 VV CC (D) 21 VV CC

36. When the system shown here is pulled by force F, the 1 kg block remains stationary relative to the wedge.There is no friction anywhere.(A) The force F is 7.5 N

37°3kg

F

1kg(B) The normal force exerted by the wedge on the block is 8 N

(C) The acceleration of the system is 815

m/s2

(D) The tension in string is 6.25 N



PHYSICS37. Three nonconducting infinite planar sheets are parallel to the y-z plane. Each sheet has a uniform surface

charge density. The first sheet, with a negative surface charge density –, passes through the x-axis at x=1m. The second sheet has an unknown surface charge density and passes through the x-axis at x = 2m. Thethird sheet has a negative surface charge density –3and passes through the x-axis at x = 4m. The netelectric field due to the sheets is zero at x = 1.5 m.

(A) The surface charge density on the second sheet is +2.

(B) The electric field at x = –2 m is i0

(C) The electric field at x = 3 m is i0

(D) The electric field at x = 6m is i–

0

38. A boat moves relative to river water with a velocity which is 'n' times the river velocity. i.e. vbR = nvr, then(A) If n < 1 boat cannot cross river.(B) If n = 1 Boat cannot cross river without drifting(C) Boat can cross river for any value of n (excluding zero)(D) If n > 1 boat can reach at just opposite point on another bank.



Matrix - Match TypeThis section contains 2 questions. Each question contains statements given in two columns, which have tobe matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II arelabelled P, Q, R, S and T. Any given statement in Column I can have correct matching with ONE OR MOREstatement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions haveto be darkened as illustrated in the following example :


P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

39. A particles is moving in a uniform circular motion on a horizontal surface. Particlesposition and velocity at time t = 0 are shown in the figure in the coordinatesystem. Which of the indicated variables in column-I is/are correctly matchedby thevariable(s) on the vertical axis in the graph(s) shown in column-II for particle's motion?

x

Column-I Column-II

(A) x component of velocity (P) t

(B) y component of force keeping particle moving (Q) t

in a circle

(C) Angular velocity of the particle (R) t

(D) X-coordinate of the particle (S) t

(T) t


PHYSICS40. Column-I Column-II

(A)

45°

A

B C

= 1.5

(P) At surface AC, TIR will take place

(B)

A

B C

= 3

60°(Q) At surface AC, light will be refracted

(C)

A

B C

= 2

45° 45°

(R) Ray refracted at AB will be parallel to base BC

(D)

A

B C

= 2

i=60°

30° 30°(S) Ray refracted at AB will not be parallel to base BC

(T) Light will graze the surface AC.





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41. Number of HI consumed whenever following compound react with Conc. HI.

O

O

42. Find out total number of compound(s) which is/are paramagnetic in natureCl2O, ClO2, ClO3, Cl2O7, K3[Co(ox)3], K3[Cr(CN)6], K2[NiCl4], K2[PtCl4], K2[NiF6]



43. How many of the following graphs are correct (Given P = pressure, V = Volume, T = Temperature, a = initialconcentration, t1/2 = Half life)

(a)

P

1/V

(At constant T & n)

(b)

V

n

(At constant T & P)

(c)

P

T(°C)

(At constant V & n)

(d)

V

T(K)

P1

P2

P > P1 2

(e)

t1/2

a(For zero order kinetics)

(f)

t1/2

Con

cent

ratio

n of

reac

tant

(For zero order kinetics)

(g)

time(For first order kinetics)

Concentrationof

product (h)

time(For zero order kinetics)

Con

cent

ratio

nof

pro

duct

CHEMISTRY



CHEMISTRY


44. 3HC CH Fe-tube

(A) CH –Cl3AlCl3

(B) NaNH3

(C)

D.B.E. value of (C) is

45. BrCH3

Alc. KOH Number of alkene obtained by E2

46. Select total number of substances which form molecular solid.White phosphorous, Red phosphorous, Black phosphorous, CO2, SiO2, Sulphur, Fullrene, Diamond, SiC


CHEMISTRY


47. For the reaction

x 24 3 2M MnO MO Mn O

If 1 mole of MnO4– oxidizes 1.67 mole of Mx+ and Mx+ converts into to MO3

–, then calculate the value of x inthe reaction ?

48. Given : fHº(BH3(g)) = 101 kJ/mol ; fHº(B2H6(g)) = 48 kJ/mol ; subHº(B(s)) = 560 kJ/mol.Bond energy of (H-H) = 440 kJ/mol. Calculate the value of Z, where

Z = 1

11 (x – y) ; B.E. (B–H–B (three centre two electron bond)) = x kJ mol–1 ; B.E. (B – H) = y kJ mol–1


CHEMISTRY




49. (1) O3

(2) Zn/H O2

H2

Ni

Conc. H PO3 4

Identify all the possible product(s) formed in the above reaction is/are :

(A) (B) (C)

CH2

(D)

50. Consider the following balanced reactions :(i) K2[PtCl4] + 2NH3 'X' + 2KCl (ii) [Pt(NH3)4](NO3)2 + 2KCl 'Y' + 2NH3 + 2KNO3

Both X and Y have same empirical formula Pt.2NH3.Cl2 and X is more soluble in polar solvent such as ehtanolwhile Y is soluble in non-polar solvent like petroleum, ether and CCl4. Complex X and Y are(A) Ionization isomers (B) Geometrical isomers(C) Solvate isomers (D) Co-ordination isomers

51. 12 g of liquid water has been added to a vessel, initially which contained dry N2(g) at 62 torr pressure.Aqueous tension of liquid water at this temperature is 38 torr.Choose correct statement(s). [Assuming temperature is constant for all the given conditions](A) Equilibrium pressure is 100 torr, if initially equilibrium is attained(B) Equilibrium pressure is 58.66 torr, when volume of vessel has been increased three fold to initial volume(C) Relative humidity inside the container decreased by 26.7% from initial value, when volume of vessel hasbeen increased three fold(D) Relative humidity inside the container is 64.7%, when volume of vessel has been increased three fold.


CHEMISTRY


52.

Cl

Cl

Mono nitration (A)CH ONa3

(B) Conc.HI (C)

Identify which type of reaction take place in formation of product A, B, C.(A) Electrophilic substitution (B) Electrophilic addition(C) Nucleophilic substitution (D) Nucleophilic addition

53. In an aqueous solution of NiCl2 , if didentate ligand, ethane-1, 2-dien(en) is progressively added in molarratios such as Ni : en : : 1 : 1, 1 : 2, 1 : 3 then three octahedron complexes x, y, z formed respectively.Select CORRECT statement(s) about x, y, z(A) Complex x has maximum value of absorbed wavelength(B) Complex y expected to be coloured(C) Complex z has maximum number of chelate rings(D) All three are paramagnetic outer orbital complexes

54. GivenHCl(aq) + NH4OH(aq) NH4Cl(aq) + H2O() + 52.5 kJCH3COOH(aq) + NH4OH(aq) CH3COONH4(aq) + H2O() + 48 kJfH[H2O()] = –286 kJ mol–1

fH[OH–(aq)] = –230 kJ mol–1

Which is/are correct statement ?(A) Enthalpy of neutralisation of HCl(aq) Vs NaOH(aq) is –57.3 kJ/mol.(B) Enthalpy of ionisation of NH4OH(aq) is 3.5 kJ/mol.(C) Enthalpy of ionisation of CH3COOH(aq) is 4.5 kJ/mol.(D) Enthalpy of ionisation of NH4OH(aq) is 4.8 kJ/mol.



CHEMISTRY

55.OH

CH3 H

OHCH3 CH3

TsCl/py (x)

Conc.H SO2 4 (y)

;

H SO2 4HgSO4

B H62 (THF)H O22 ,NaOH

(a)

(b)

Find the relationship in between (x) and (y), (a) and (b)(A) Identical, (x) and (y) (B) Position isomer, (x) and (y)(C) Identical, (a) and (b) (D) Position isomer, (a) and (b)

56. Which is/are correct statement ?(A) Endothermic reaction is non spontaneous at all temperature, if rS is negative.(B) Exothermic reaction is spontaneous at all temperature, if rS is negative.(C) Enthalpy of endothermic reaction always increase, when temperature of reaction increase.(D) For exothermic reaction change in entropy of surrounding is positive.



CHEMISTRY57. Consider T-S diagram of one reversible carnot engine given as following :

A B

D

T(K)1000

400

300 400

S(JK )–1

Which is/are correct statement ?(A) Efficiency of carnot engine is 0.6.(B) Heat taken from the source is 100 kJ.(C) Work done by carnot engine is – 40 kJ.(D) Number of cycle perform by carnot engine is 10 in order to obtained 600 kJ of energy.

58. A complex having molecular formula Cr(CO)2(CN)2(NH3)py has been synthesized, which shows one band ofC – O stretching and one band of C – N stretching in infrared spectrum. What is/are most likely structure(s)of this complex

(A) CrNH3OC

OCCN–

CN–

py(B) Cr

py

OC

OC

CN–CN–

NH3

(C) CrCO

OCCN–

CN–NH3

py(D) Cr

CO

py CN–

CO

CN–H3N





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

59. Column-I Column-IICompound

(A)OOH

H SO2 4 (P) Rearrangement reaction

(B)

Br

H O2 (Q) E1

(C)H SO /2 4

OH(R) SN1

(D) RSNa

Br

DMSO(S) SN2

(T) Racimic mixture can formedas product


CHEMISTRY


60. Column-I Column-IIProperties of product(s)

(A) 3 2Pb(NO ) (P) Coloured/black species

(B) 2 3Ag CO (Q) Diamagnetic gas

(C) 2 4 3Cr (SO ) (R) Acidic gas

(D) 2 4BeC O (S) Colourless gas

(T) Water insoluble species


CHEMISTRY



CODE - ADATE : 28-06-15

B. Question paper format :9. The question paper consists of 3 parts (Mathematics, Physics and Chemistry).

Each part has 3 sections.

10. Section I contains 8 questions. The answer to each of the questions is aninteger, ranging from 0 to 9. The answer will have to be appropriately bubbled in theORS as per the instructions given at the beginning of the section.



C. Marking Scheme :

13. For each question in Section-I, you will be awarded 4 marks if you darken thebubble corresponding to the correct answer and zero mark if no bubbles is darkened.No negative marks will be awarded for in this Section.

14. For each question in Section-II, you will be awarded 4 marks if you have darkenedonly the bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. In all other cases, minus two (–2) mark will be awarded.

15. For each question in Section III, you will be awarded 2 marks for each row inwhich you have darkened the bubble(s) corresponding to the correct answer and zeromark if no bubbles are darkened. In all other cases, minus one (–1) mark will beawarded. Thus, each question in this section carries a maximum of 8 marks.




















CODE - A


DATE : 28-06-15




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1. Let , are the roots of the quadratic equation ax2 + bx + c = 0, where = 4 ( > 0). If 3a = 2(c – b) and

0r

r )(S , then find the value of 6S.

2. Let f(x) be periodic function with fundamental period 12. If 9dx)x(f12

6–

and 12dx)x(f12

0

, then find dx)x(f31

6

0 .



MATHEMATICS


3. Let a function 'f' defined from R R as

2x5Px2xPx)x(f

2. If the function f is surjective, then the last digit

of sum of all possible integeral values of P in [–100, 100] is

4. Let f be a function defined by x1

1xxf

x R – {0, 1}. If f(sec2) = g(), where

,

22,0 ,

then the value of

0)(g21

d is

m

, m R. Find the value of m2.

5. Let S1 : x2 + (y – 4)2 = 12 and S2 : (x – 3)2 + y2 = 13 be two circles intersecting at A and B. A quadrilateral

ABCD is formed by tangents at A and B to both circles. Find the diameter of circumcircle of quadrilateralABCD.


MATHEMATICS


6. Let KxxKx4xKx4Kx

Kx4Kxx)x(f

2

2

2

. If f(x) is positive for all x R, then find the number of integral values in the

range of K.

7. Let

3

2/3

2

(x 1) –2 x –1

f(x) x – 1 –1 x 1

–(x – 1) 1 x 2

, then find the total number of points in (–2, 2) at which f attains either a

local maximum or a local minimum.

8. Consider the infinite series 1 + 3x + 7x2 + 15x3 + ...... + (1 + 2 + 22 + .... 2n) xn + ..... whose sum is defined

if 21x

21– . If the value of the sum is 3

8 when x = x0 then find the value of 24x0 is


MATHEMATICS




9. Let f(x) be continuous and strictly increasing function of x and suppose F(x) = 1 + f(x) + (f(x))2 + (f(x))3.If F(x) has a positive root then(A) F(x) is a decreasing function of x (B) f(0) < – 1(C) |f(0)| < 1 (D) F(0) < 0

10. The function f(x) = a(x2 – 1)(ax + b), a 0 has(A) A point of local maxima at certain x R+ (B) A point of local minima at certain x R+

(C) A point of local maxima at certain x R– (D) A point of local minima at x = 1 if a + b = 0

11. If x is real, then expression (x a)(x b)

(x c)

will assume all real values if

(A) a > b > c (B) a < c < b (C) a > c > b (D) b > a > c


MATHEMATICS


12. If the expression 1mx 1x

is non negative x > 0, then the value of m can be

(A) 12

(B) 0 (C) 14

(D) 12

13. Identify the correct statement(s)(A) Number of ways of distributing 6 distinct toys between 3 children equally is 90(B) Number ways of distributing 6 identical toys between 3 children if each child gets none, one or more toysis 28(C) Number of ways of placing 5 letters in 5 directed envelopes so that exactly 2 letters are in the rightenvelope is 40(D) If a regular polygon has 54 diagonals, then numbers of sides of polygon is 10

14. If ax2 + 2bx + c = 0, b 21

be an equation with integral coefficients, then the equation

b2x2 – (b2 – ac)x – ac = 0 must have(A) Two integral roots (B) Two rational roots(C) Two irrational roots (D) One integral root independent of a, b, c


MATHEMATICS


15. The value of

xcot

e/12

xtan

e/12 )t1(t

dt)t1(

dtt, is

(A) xtan2

12

(B) xcos1

xcos2

2

(C) 1 (D)

1

1–2t1

dt2

16. Let P(x) be a polynomial of 'n' degree and

0x,0

0x,ex1P)x(f

4x1–

3 , then

(A) f(x) is discontinuous at x = 0 (B) f(x) is continuous at x = 0

(C) f(x) is non-differentiable at x = 0 (D) f '(0) = )x(flim0x



MATHEMATICSSECTION - III

Comprehension TypeThis section contains 2 groups of questions. Each group has 2 multiple choice questions based on aparagraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MOREis/are correct.


Consider

0xx0x|1x|

)x(f ,

1x|2–x|–1x1|x|

)x(g and h(x) = f(x) + g(x)

17. Which one of the following statement(s) is/are correct

(A) h(x) increases in (–, –1) and decreases in (1, )

(B) h(x) decreases in (–, –1) and increases in (1, )

(C) h(x) has local minimum at x = 1

(D) h(x) has local maximum at x = 1

18. Which of following statement(s) is/are correct

(A) h(x) is non differentiable at 4 points x R (B) h(x) is discontinuous at 2 points x R

(C) h(x) has no global minimum value x R (D) h(x) is non-differentiable at 3 points x R


Paragraph for Question Nos. 19 to 20Consider f : R R be a polynomial function whose degree is greater than 1 and at most 4. Also f is a one-

one and onto function whose graph is symmetrical about A(4, 0) and f has horizontal tangent at x = 4

19. Which of the following statement(s) is/are correct

(A) f–1(2) + f–1(–2) = 8 (B) f(6) + f(2) = 0

(C) f–1(1) + f–1(–1) = 4 (D) f "(7) + f "(1) = 0

20. If f '(10) = 20, then f '(–2) is equal to

(A) 4 (B) 8 (C) 20 (D) 32


MATHEMATICS




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21. Behind a equiconvex converging lens having both the surfaces of the same radius 10cm, a plane mirror hasbeen placed. The image of an object at a distance 40 cm from the lens is formed at the same position. If aliquid of refractive index = 2 is filled between lens and mirror, find the distance of image from mirror. (mirror

and lens or this). If the distance is 40x

cm, find x.

O

22. A fixed point charge Q is at origin. At t = 0, a charge q with mass m is at x = a with leftward velocity V0 which

satisfies 20

kQq 3mVa

. The particle turns around and starts to move rightward at the position b < a. If the

speed of particle at infinity is 0V n . Find n.



PHYSICS

23. In the figure shown, friction force between the bead and the light string is mg4

, find the time in which the bead

looses contact with the string after the system is released from rest. If this time t = x 27g

, Find x.

m

m

24. One end of an spring of force constant k1 is attached to the ceiling of an elevator. A block of mass 1.5 kg isattached to lower end of spring. Another spring of force constant 'k2' is attached to the bottom of the massand to the floor of the elevator as shown in figure. At equilibrium, the deformation in both the spring are equaland is 40cm. If the elevator moves with constant acceleration upward, the additional deformation in both thesprings have 8cm. Find the elevator's acceleration (in m/s2) (g=10ms–2)

k1

k2

25. A balloon leaves the ground at time t = 0 with an upward acceleration of 3m/s2. When it is at height 54m fromground, a light stone is dropped from it. Find the distance (in m) between baloon and stone at t = 9 sec. If this

distance is 351x

meter. Find x. Acceleration of balloon remains same after drop of stone.



PHYSICS


26. Electric field at a point (x,y,z) in space is given by 2E (y )i 2yx j volt/metre. Assuming electric potential

at origin to be zero, find the potential (in volt) at (–1m, –3m).

27. A gas undergoes a process such that P 1/T2. The molar heat capacity for this process isC = 49.88 J/mol–K. Some heat is given to 1 mole of this gas at constant volume to raise the temperature by1ºC. If the amount of this heat is equal to x(R), find x (R is universal gas constant)

28. The maximum and minimum distances of a planet from the centre of the sun are 2R and 4R respectively,

where R is radius of sun. If radius of curvature at point of minimum distance is 5 x R3

. Find x


PHYSICS




29. Two dipoles of dipole moments p each are placed on points A (a, 0) and B(–a,0) as shown in figure. Choosethe correct options(s)

(A) Work done in rotating both dipoles by 90º clockwise is 2

4kpr

y

O xB A(B) Work done in rotating both dipoles by 90º clockwise is zero(C) Electric field at origin is zero(D) Magnitude of electric fields due to both dipoles at origin is zero.

30. A stretched string, fixed at both ends, vibrates at frequency of 12 Hz with standing wave pattern as shown infigure

Select the correct alternative(A) The fundamental frequency is 6Hz (B) The fundamental frequency is 4Hz(C) The frequency of first overtone is 8 Hz (D) The frequency of first overtone is 6Hz

31. Select the correct option for the adjoining situation in which liquid is flowing through a pipe of variable cross-section (P1, P2 represent pressure)

v1 v2

L1 L2

P1 P2

(A) v1 > v2 if L1 > L2 (B) v1 < v2 for all values of L1 and L2

(C) P1 < P2 for all values of L1 and L2 (D) P1 > P2 for all values of L1 and L2


PHYSICS


32. A lift is moving down with an acceleration 20 m/s2. Which of the following is/are NOT true ?

5kg

30º 20 m/s2

(A) Acceleration of 5 kg block along incline is 15 m/s2

(B) Normal force is 25 3 and acceleration is 5m/s2 along incline

(C) Normal force is zero(D) Acceleration of 5 kg is 20 m/s2 downwards

33. In the YDSE arrangement shown here, the screen starts moving towards right with speed v at t = 0, asshown. Position of any point B on the screen can be specified by y or by angle as shown. Choose thecorrect statement(s)

B

Ay

Screen(at t = 0)

dsource( )

X

(A) At any point on the screen (for a given y) fringe order decreases with time(B) At any point B on the screen (for a given ) fringe order remains constant(C) At any point B on the screen (for a given y), at t = 0, 3rd order minima was positioned. After some time,

3rd order maxima may be positioned at that point(D) Point (for a given y), where 3rd order maxima is positioned at t = 0, 2nd order minima is positioned at time

t = xv


PHYSICS


34. A thin semicircular rod of plastic having uniform charge per unit length is placed on a smooth horizontalsurface and it is tied by two insulating threads as shown. A point charge q is held at rest at the centre of thering by applying a force F. Which of the following statements is correct ?

(A) 0

qF2 R

Insulatingthreads

R q

F

T T (Tension)

(B) F = 0

(C) 0

qT2 R

(D) 0

qT4 R

35. A black body emits maximum radiation near a wavelength m. The emissivity of the material is 0.7. If theabsolute temperature of the black body is doubled, then(A) the total emitted energy increases 8 times (B) the total emitted energy increases 16 times

(C) the maximum radiation occurs at 2m (D) the maximum radiation occurs at m12

36. A ray of light is incident grazingly on face AB of a right angled prism as shown. It emerges out of face AC, asshown, e = Angle of emergenece. Refractive indices of different media have been shown in the diagram.Choose the correct alternatives

Aire

A

µ2

B C

µ1

(A) µ12 + sin2e = µ2

2

(B) µ22 + sin2e = µ1

2

(C) µ12 + cos2e = µ2

2

(D) If the ray just fails to emerge out of the face AC of the prism, for µ2 = 3 , angle of refraction at face AB

is 1 2sin3


PHYSICS


SECTION - IIIComprehension Type

This section contains 2 groups of questions. Each group has 2 multiple choice questions based on aparagraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MOREis/are correct.


A spherical capacitor consists of a spherical shell of radius b. This is concentric with a smaller conducting

sphere of radius a.

ba

37. If charge given to inner sphere is q then what should be charge on outer sphere so that potential energy ofsystem is minimum

(A) q (B) – q (C) q b

a

(D) aqb

38. If charge on outer sphere is Q and inner sphere is earthed then which of the following is a correct statement(A) field outside (r > b) is zero (B) charge on inner sphere is zero(C) field at point between two sphere is zero (D) None of these



PHYSICSParagraph for Question Nos. 39 to 40

Parallel rays of wavelength = 4500 Å (in medium of refractive index µ1 = 43 ) are incident on the two slits of

Young's double slit experiment. the space between the slits and the screen is filled with a material of

refractive index µ2 = 53 . A glass slab of thickness 10µm and refractive indes µg =

32

is placed before S2.

Distance between the slits is 0.5 mm and between the slits and the screen = 1m.

S1

S2 O

D

39. Find the position of central maxima from O(A) 2mm (B) 5mm (C) 8mm (D) None of these

40. Find the ratio of the intensities at O and at central maxima

(A) 2 25cos

9

(B) 2 30cos

9

(C) 2 25cos

18

(D) 2 30cos

18




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

41.Acid catalytic

Hydration(x)

OHTotal number ofstructural isomeric

alkene

Find the value of x.

42. Find out total number of electrons of Co2+ ion which are present in non axial d-orbitals in the complexcompound : [Co(dmg)2]



CHEMISTRY43. Given : rG for X(, 1 atm 200 K) X(g, 1atm 200 K)

vapH(X, 400 K) = 100 kJ mol–1 ; Cpm(X, ) = 180 Jk–1 mol–1

Cpm(X, g) = 80 Jk–1 mol–1 ; B.P. of X() = 400 K, ln 2 = 0.7

Calculate the value of Z. where Z = –1

rG(inkJ mol )8

44. The number of resonance structures for N is

OHNaOH N

45. 100 ml 0.15 M solution of CoCl3.xNH3 was treated with excess of AgNO3 solution and 0.03 moles of AgClwas obtained, then find out value of x.



CHEMISTRY


46. Given : Bond energy (in kJ mol–1)C – H : 410 ; C – O : 350 ; O – H : 460vapH (CH3OH()) = 35 kJ mol–1

If the enthalpy of atomisation of CH3OH() is X (kJ mol–1), than calculate the value of X

415

47. The number of hydroxyl group(s) in Q is

H

HO

H+

heat P(Major)

aqueous dilute KMnO (excess)4

0°CQOH

H

48. Which of the following compound(s) is/are white and water insoluble.BaCO3, Fe2O3, AgBr, PbCrO4, CaC2O4, BaCl2, KMnO4, Na2CrO4, Pb(CH3COO)2,


CHEMISTRY




49. Which is/are correct statement ?

(A) np value increase when K-shell electron capture takes place.

(B) np value increase when -emission takes place.

(C) C146 present in very small amount in nature due to radioactivity..

(D) C146 can not be used to find the age of living materials.

50. Aqueous solution of NH3 gas is basic because.

(A) NH3 undergoes self dissociation in water

(B) NH3 acts as electrolyte in water

(C) NH4+ ion forms stronger hydrogen bond with water than NH3 molecule does with water

(D) NH3 molecules reduce concentration of H+ ions that are furnished from H2O.

51. CH3 – C C – CH3 4

2BaSOPd

H

(A)

4

2CCl

Br (B) ;

CH3 – C C – CH3 3NH.liq

Na (C) 4

2CCl

Br (D)

Relation between (A) and (C), (B) and (D)(A) Identical, Identical (B) Identical, Diastereomer(C) Diastereomer, Identical (D) Diastereomer, Diastereomer


CHEMISTRY


52. d-orbitals of metal lose their degeneracy in(A) Blue vitriol (B) Anhydrous CuSO4

(C) Potassium ferrocyanide (D) Potassium ferricyanide

53. The observed rate of a chemical reaction is substantially lower than the collision frequency. Which is/arecorrect statement about for this fact?(A) The reactants do not have the required energy(B) The reactants do not colloid in the proper orientation(C) Collision complex exists for a very short time(D) Collision frequency overestimates the number of effective collisions

54.

PhOH OH

OCH3 CH3

( )I

( )II ( )III

( )IVCH3

H

Major product

Which group prefer 1,2-shift in pinacolone rearrangement.(A) I (B) II (C) III (D) IV


CHEMISTRY


55. Identify which reactant give CH3COCHO as product by ozonolysis

(A) (B) (C) (D)

56. For the reaction A(g) B(g) + C2

(g), H = +ve

The correct statement(s) is/are(A) Kp > Kc at 10 K temperature(B) Unit of KC is mol0.5 litre–0.5

(C) Equilibrium shifts forward direction when temperature increased(D) Equilibrium shifts backward direction when volume decreased


CHEMISTRYSECTION - III

Comprehension TypeThis section contains 2 groups of questions. Each group has 2 multiple choice questions based on aparagraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MOREis/are correct.


For a reversible reaction A B C D the free energy change (G) and standard free energy change

(G°) are related with each other by following relation.G = G° + RTlnQc

When 'R' = Universal gas constant, T = Temperature in Kelvin

Qc = reaction quotient = [C][D][A][B] and at equilibrium, QC = Keq (Equilibrium constant)

The value of Keq can give an idea about the extent of completion of a chemical reaction before the equilibriumis attained.Now, answer the following questions

57. Which of the following graph represent that reacting species of a chemical reaction are almost completelyconsumed?

(A) G

Reactant (R) Product (P)

Extent of reaction

(B) G

Reactant (R)

Product (P)

Extent of reaction

(C)

G

Reactant (R)

Product (P)

Extent of reaction

(D)

Reactant (R)Product (P)

Extent of reaction

G

58. Acetic acid can form a dimer in the gas phase. The dimer is held together by two H-bonds with a totalstrength of 66.5 KJ mol–1 of dimer at standard -states. If at 25°C, the equilibrium constant for the dimerisationis 1 × 103, then, standard entropy change (S°) for the reaction 2CH3COOH CH3(OOH)2 is :(A) – 0.764 kJ/K (B) – 0.163 kJ/K (C) – 0.980 kJ/K (D) – 0.264 kJ/K


Paragraph for Question Nos. 59 to 60Formation of complex compounds is one of the most important properties of d-block metal cations. Among

various theories of bonding of Co-ordination Compounds, two theories : Valence Bond Theory and Crsytal

Field Theory play very important roles in determining geometry of a complex ion/compound and electronic

distribution of d orbitals of central metal atom/ion in presence of given ligands respectively. A very important

property of complex ion/compound is to exhibit isomerism.

59. Which of the following complex ion(s) is/are inner orbital complex as well as low spin complex ion(s)

(A) [Cu(NH3)4]2+ (B) [IrF6]

3– (C) [Ag(S2O3)2]3– (D) [Ni(CN)5]

3–

60. Which of the following complex compound(s) can exhibit at least two types of structural isomerism.

(A) [PdBr(NO2)(NH3)4] (C2O4) (B) [Co(SCN)(H2O)5]Br2

(C) [Cr(NH3)6][Co(ONO)6] (D) K[Fe(CN)2(H2O)4]


CHEMISTRY



CODE - A



10. Section I contains 8 questions. The answer to each of the questions is aninteger, ranging from 0 to 9. The answer will have to be appropriately bubbled in theORS as per the instructions given at the beginning of the section.


12. Section III contains 2 groups of questions. Each groups has 2 questions based on aparagraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out ofwhich one or more is/are correct.

C. Marking Scheme :

13. For each question in Section-I, you will be awarded 4 marks if you darken thebubble corresponding to the correct answer and zero mark if no bubbles is darkened.No negative marks will be awarded for in this Section.

14. For each question in Section-II, you will be awarded 4 marks if you have darkenedonly the bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. In all other cases, minus two (–2) mark will be awarded.

15. For each question in Section-III, you will be awarded 4 marks if you have darkenedonly the bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. In all other cases, minus two (–2) mark will be awarded.

DATE : 28-06-15




















CODE - A


DATE : 26-07-15




1. The solution of the differential equation 1–x1siny–

x1cos

dxdyx2

where 1–)x(ylimx

is

(A)

x1sin

1x–y (B)

x1cos–

x1siny

(C)

x1cos–

1xxy 2 (D)

x1cos–

x1sin2y

2. Solution of the differential equation 22233 x–yyydxdyx

(A) y + x2 – y2 = cxy (B) cxx–yy 22 (C) cxyx–yy 22 (D) cxyx–yx 22

3. The value of the definite integral dx)xtan1ln()x4–x(4/

0

2

is

(A) 48

2ln3(B)

1922ln3

(C) 64

2ln3(D)

1282ln3

4. If (1 – p) is a root of quadratic equation x2 + px + (1 – p) = 0 then its roots are(A) 0, 1 (B) –1, 1 (C) 0, –1 (D) –1, 2



MATHEMATICS


5. Number of ways to arrange the letters of the word PECULIAR with the vowels in alphabetical order?(A) 70 (B) 1680 (C) 360 (D) 480

6. The co-efficient of xn in the expension of (1 + x) (1 – x)n is(A) n – 1 (B) (–1)n (1 – n) (C) (–1)n – 1 (n – 1)2 (D) (–1)n – 1 . n

7. If )0x(ex.......yeyey

then dxdy

is

(A) x1

x

(B) x1

(C) x

x1(D)

xx1

8. A family of lines is given by (1 – 2)x + (1 + )y + 2 = 0 where be a parameter. The line of this family whichis at a maximum distance from the point (2, 4) is(A) x – 2y + 4 = 0 (B) 6x + 21y + 10 = 0 (C) 6x – 21y + 10 = 0 (D) 12x – 42y + 19 = 0


MATHEMATICS



This section contains 2 groups of questions. Each group has 3 multiple choice questions based on aparagraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE iscorrect.


Let f be a differentiable function satisfying 0dt))t(f–t(cos–dt)t(fx

0

)x(f

0

1– and f(0) = 1

9. The number of solution(s) of the equation 02xsin

)x(f)x2(f in (0, 2) is

(A) 2 (B) 3 (C) 4 (D) 5

10. The value of dx)x(f2/

0

lies in the interval

(A)

1,2(B) 1,

2

(C) 3 ,2 2

(D)

2,0

11. The value of

)x100(f

x100cos......)x2(fx2cos

)x(fxcoslim

0x is equal to (where [·] denotes GIF)

(A) 0 (B) 4950 (C) 5049 (D) 5050


MATHEMATICS



Let 1–|3x|2–|x|)x(f

12. Gradient of the curve where it crosses the axis of x

(A) 21

(B) 31

(C) 41

(D) 32

13. Number of points in domain of f(x) where f(x) is non-differentiable(A) 0 (B) 2 (C) 3 (D) 4

14. Area bounded by f(x) with co-ordinate axes in fourth quadrant (x > 0 , f(x) < 0)(A) 3 – ln4 (B) 3 – 2 ln2 (C) 4 – 2 ln2 (D) 2 – 4 ln2


MATHEMATICS




15. Let

0x0x0x

;;;

x0

e)x(f

2

x1x2

which of the following statement(s) is/are correct?(A) f(x) is continuous at x = 0 (B) f(x) is derivable at x = 0(C) f(x) is discontinuous at x = 0 (D) f(x) is non-derivable at x = 0

16. Let x

x11)x(f

and

1x

x11)x(g

both functions defined for x > 0. Which of the following statement

is/are correct?(A) f(x) is increasing function (B) g(x) is increasing function(C) f(x) is decreasing function (D) g(x) is decreasing function


MATHEMATICS


17. Let f(x) = min ((t) , –3 t x) x [–3, )where (x) = ||x – 1| – |x + 1||, then(A) f(x) is non differentiable at x = –1, 0 (B) f(x) is non differentiable at x = –1, 1

(C) f(100) = 0 (D)

10

3

5dx)x(f

18. Let R be the region containing the point (x, y) on x-y plane such that 2 |x + 3y| + |x – y| 4 then(A) R is enclosed between two rectangles (B) R is enclosed between two parallelogram(C) Area of R is 6 unit (D) Area of R is 8 unit


MATHEMATICS


SECTION - IVMatrix - Match Type



P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

19. Column I Column II(A) If A and B are two matrices of order 3 such that AB = 0 and A2 + B = I; (P) 0

then tr(A2 + B2) is equal to (tr(P) denotes the trace of matrix P)(B) Let y = f(x) satisfy the differential equation y lny + xy' = 0 where y(1) = e (Q) 1

and xlim x(f(x) – 1) e

; then equals

(C) If

dxedx2e2

e1

)e–x(loge

1

xln 2 then [] equals to ([·] denotes GIF) (R) 2

(D) If P( + 1, – 3) be any point in xy plane, then the integral values of (S) 3for which the point P may lies on the lines or between the linesx + 2y = 1 and 2x + 4y = 14 is (T) 4


MATHEMATICS


20. Column I Column II

(A) Let f(x) is a derivable function satisfying dt)t–xsin(e)x(fx

0

t and (P) –1

g(x) = f"(x) – f(x) then the possible integers in the range of g(x) is(B) If subsitution x = tan–1(t) transform the differential equation (Q) 0

0xsecdxdyxy

dxyd 22

2 into k

dtdy))t(tanyt2(

dtyd)t1( 1–2

22

then k equals(C) If a2 + b2 = 1 (a, b R) then a3b – ab3 may equals to (R) 1(D) If the system of equations x – y – z = 0 ; x – y – z = 0 ; x + y – z = 0 (S) 2

has a unique solution, then the value of can be(T) 3




21. In the circuit shown in figure, equivalent resistance between A and B is :(A) 8(B) 15

(C) 32

AB

2

(D) 2

22. A galvanometer of coil resistance 1 is converted into voltmeter by using a resistance of 5 in series andsame galvanometer is converted into ammeter by using a shunt of 1. Now ammeter and voltmeter areconnected in circuit as shown, find the reading of voltmeter and ammeter.

124.5

V

15 15 6

A30V

(A) 3 volt, 3 amp (B) 2 Volt, 2 amp (C) 4 Volt, 3 amp (D) 3 Volt, 4 amp

23. In an experiment to measure the internal resistance of a cell by a potentiometer, it is found that the balancepoint is at a length of 2m when the cell is shunted by a 5 resistance and at a length of 3m when the cell isshunted by a 10 resistance. The internal resistance (r') of the cell is :

Gr'

r

'

(A) 1.5 (B) 10 (C) 15 (D) 1



PHYSICS


24. In the circuit shown in figure if switch S is closed, the charge that flows through battery is equal to :

+ –+ –+ –

3 F(initially

uncharged)

15 C,3 F

10 V

S

(A) 5 C (B) 7.5 C (C) 10 C (D) 15 C

25. A capacitor is to be designed to operate, with constant capacitance, in an environment of fluctuating tem-perature. As shown in the figure, the capacitor is a parallel plate capacitor with 'spacer' to change thedistance for compensation of temperature effect. If 1 be the co-efficient of linear expansion of plates and 2

that of spacer, the condition for no change in capacitance with small change of temperature is (The capaci-tance of the capacitor is equal to C and spacer have insulated ends. Assume K of spacer to be = 1).

Spacer

(A) 1 = 2 (B) 1 = 22 (C) 21 = 2 (D) 21 = 32


PHYSICS


26. A cylindrical conductor AB of length l and area of cross-section a is connected to a battery having emf E and

negligible internal resistance. The specific conductivity of cylindrical conductor varies as = 0 ,xl

where

0 is constant and x is distance from end A. What is the electric field just near the end B of cylinder ?

(A) El

(B) 3E2l

(C) 2E3l

(D) E2l

E

A B

27. The air in a open pipe of length 36 cm long is vibrating with 3 nodes and 2 antinodes. The temperature of theair inside the pipe is 51ºC. What is the wavelength of waves produced in air outside the tube where thetemperature of air is 16ºC ?(A) 32.1 cm (B) 68 cm (C) 34 cm (D) 10.2 cm

28. A solid sphere of radius R made of a material of Bulk modulus K is surrounded by a liquid in a cylindricalcontainer. A light piston of area A floats on the surface of the liquid. When a mass m is placed on the pistonto compress the liquid, the fractional change in the radius of the sphere will be :

(A) mgAK

(B) 3mgAK

(C) mg

3AK (D) mg2AK


PHYSICS




Paragraph for Question Nos. 29 to 31If a system is in equilibrium as shown in diagram. Choose the correct option if ONLY the mentioned elementis cut. Consider springs and string to be ideal and both springs are identical.

(1)

mA

2mB

3mC

(2)

29. Acceleration of block A just after string is cut is :(A) g (B) 2g (C) 4g (D) 5g

30. Acceleration of block B just after spring 1 is cut is :(A) g (B) 2g (C) 4g (D) 5g

31. Tension in string, just after spring 2 is cut is :(A) Zero (B) mg (C) 2mg (D) 4mg


PHYSICS


Paragraph for Question Nos. 32 to 34When the capacitor A is filled with a dielectric (K = 2) it has capacitance C1 = 2 F as circuit shown.Capacitors B and C are air capacitors and have capacitances C2 = 2F and C3 = 4F respectively.

S1 S2

B

C

E=180V+– A

32. Find charge on capacitor A when only S1 is closed and S2 is open(A) 144 C (B) 360 C (C) 180 C (D) 420 C

33. If both switches S1 and S2 are closed the charge on capacitor C2 will be(A) 144 C (B) 360 C (C) 180 C (D) 240 C

34. If keeping X1 and X2 closed the dielectric slab of A is removed then charge that slows, through the battery will be.(A) 144 C (B) 360 C (C) 180 C (D) 240 C





35. A uniform wire of resistance R is shaped into a regular n-sided polygon (n is even). The equivalent resistancebetween any two corners can have

(A) The maximum value R4

(B) The maximum value Rn

(C) The minimum value 2n – 1Rn

(D) The minimum value Rn

36. Two spherical planets have the same mass but densities in the ratio 1 : 8. For these planets, the(A) Acceleration due to gravity on surfaces will be in the ratio 1 : 1.(B) Acceleration due to gravity on surfaces will be in the ratio 1 : 4.(C) Escape velocities from their surfaces will be in the ratio 1 : 2.

(D) Escape velocities from their surfaces will be in the ratio 1: 2 .



PHYSICS37. A particle vibrates in SHM along a straight line. Its greatest acceleration is 52 cm s–2 and when its distance

from the equilibrium position is 4 cm, the velocity of the particle is 3 cms–1. Then mark the correct option(s).(A) The amplitude is 10 cm (B) The period of oscillation 2 sec(C) The amplitude is 5 cm (D) The period of oscillation 4 sec

38. In the circuit shown in figure :(A) i = 2.5 A when S1 is closed and S2 is open.

(B) i = 203 A when S1 is open and S2 is closed.

(C) i = 53 A when S1 and S2 both are open.

S1 S2

1 2 10V 3

20Vi

(D) i = 20A when both S1 and S2 are closed


PHYSICSSECTION - IV



P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

39. A uniformly charged non-conducting uniform hollow sphere of radius 1m and mass 2kg having angular speed0 = 9 rad/s is gently placed on non-conducting rough horizontal surface with coefficient of friction at t = 0.Charge on the sphere is Q0 and uniform elelctric field E is present in the region parallel to horizontal surface.(Given Q0E = 10 N, g = 10 ms–2). Then match the column

E x

y

++++++

+++++++++++++

0

Column-I Column-II(A) If = 0.6, then acm at t = 1 second (P) Along +ve x-axis(B) If = 0.4, then acm at t = 1 second (Q) Along –ve x-axis(C) If = 0.5, then acm at t = 1 second (R) Zero(D) If = 0.6, then friction force at t = 1 second (S) Non-zero

(T) Data Insufficient



PHYSICS


40. Consider an imaginary cylindrical surface of length 3R and radius R. A point charge q is placed at the axis ofcylinder at a distance of 2R from plane circular face F2 and at R from plane circular face F1.

F1F2

q

R

Column-I Column-II

(A) Electric flux through face F1 is (P)0

q 1 12 2 5

(B) Electric flux through face F2 is (Q)0

q 212 5

(C) Electric flux through curved surface of cylinder is (R)0

q 11–2 2

(D) Total flux through the cylinder is (S)0

q 21–2 5

(T)0

q




41. Which of the following hydrate isomer of CrCl3.6H2O absorb shorter wavelength in visible spectrum :(A) [Cr(H2O)6]Cl3 (B) [CrCl(H2O)5]Cl2.H2O (C) [CrCl2(H2O)4]Cl.2H2O (D) [CrCl3(H2O)3].3H2O

42. The amount of 6C14 isotope in a piece of wood is found to one sixteenth (1/16) of that present in a fresh pieceof wood. Calculate the age of the piece of wood (t1/2 of 6C14 = 5770 years)(A) 7999 years (B) 11540 years (C) 16320 years (D) 23080 years

43. Number of RMgX consumed during reaction are ?

OH

C – Cl

O

COCH3O

1. RMgX(excess)2. H O3

+

(A) 2 (B) 3 (C) 4 (D) 5

44. In which of the following compound on thermal decomposition, formed metal oxide is not affected by presenceof oxygen (air) :(A) FeCO3 (B) SnC2O4 (C) FeC2O4 (D) CuSO4



CHEMISTRY


45. Identify compound (A) in the following equilibrium.

A HO

OHOH

(A) OH

OHO (B)

OHO

OH

(C) O

HOOH

(D) OH

HOOH

46. Which of the following ore is present in least abundance in earth crust :(A) PbS (B) Fe2O3 (C) KNO3 (D) SnO2

47. Calculate EMF of represented cell at 25ºC

)s(Ag|)s(AgCl|)aq(HCl|)g(Cl|)s(PtM1.0bar1.0

2

[Given : 06.0F

RT303.2 ; Ksp (AgCl) = 10–10 ; SRP values : –2

o oAg |Ag Cl |ClE 0.80V ; E 1.36V ]

(A) 1.59 V (B) –1.19 V (C) 1.19 V (D) –1.13 V

48. Number of diastereomeric pair formed in product B.

OH

H / (A) HBrCCl4

(B)(major)

(A) 2 (B) 3 (C) 4 (D) 6


CHEMISTRY




Paragraph for Question Nos. 49 to 51Extraction of pure metal from its ore is completed through various stages like concentration of ore, conversionof concentrated ore into metal oxide etc concentration of ore can be carried out by physical as well aschemical methods.

49. INCORRECT statement for Froth Floatation process is :(A) Pine oil increases non-wettability of sulphide ores with water.(B) Two different sulphide ores can be separated by adjusting proportion of oil to water(C) PbS form water soluble cyano complex with depressant NaCN in presence of ZnS.(D) Sulphide ores are attached to outer layer of air bubble

50. INCORRECT statement for leaching is :(A) It is commercially used for ores of Ag, Au, Al.(B) Silver and gold ores are leached out in the form of water soluble complex ions(C) In Bayer's process Fe2O3 does not react with leaching reagent(D) Complete precipitate of Al(OH)3 is obtained by adding conc. HCl into NaAlO2 solution

51. INCORRECT statement for Roasting and calcination is :(A) Both are carried out to convert concentrated ore into metal oxide.(B) After calcination ore becomes porus(C) During roasting SO2(g) is mainly released(D) Both calcination and roasting are exothermic reactions


CHEMISTRYParagraph for Question Nos. 52 to 54

A Grignard reaction is carried out by starting with the preparation of the organomagnesium reagent, RMgX,from metallic Mg and the haloalkane (RX) in ether and a solution of the carbonyl compound in ether is thenadded, all under rigorously anhydrous conditions. The overall reactions is completed by the aqueous acidicquench.The reactions of Grignard reagents with aldehydes and ketones give alcohols depending on the pattern ofalkyl/aryl substitution on the carbonyl carbon. The reaction with esters is slightly different. This is due to thenature of the tetrahedral intermediate (alkoxide) initially formed by addition of RMgX to the ester. We alsoobserve reactions of Grignard reagent with N, N-dimethylamide, carbon dioxide; oxiranes (epoxides) etc.

52. Identify which product give lucas test with HCl + ZnCl2.

(A)

OH

1.PhMgBr2.H O3

(B) 1. PhMgBr2. H O3

C

O

O

(C) 1.PhMgBr2.H O3

O

(D) 1.PhMgBr (1 mole)2.H O3

O

Cl

53.

OH

1. CH MgBr (excess)3

2. H O3

O

C – Cl

O

Cl

Identify product

(A)

OCH3

C – CH3

O

OH

(B)

OCH3

HO

OH

(C)

CH3

HO

CH3OHOH

(D)

CH3

O

CH3HO

CH3

HO

54. O3Zn (A)

(1) CH MgBr (excess)

(2) H O3

3

(B)

Which statement is true for the above reaction(A) One mole of CH3MgBr consumed. (B) ketone reacts faster than aldehyde.(C) Product has two alcohol groups (D) Acetal is formed


CHEMISTRY




55. A real gas can be liquefied at(A) Above critical pressure and below critical temperature(B) Above critical temperature and above critical pressure(C) Below critical temperature and pressure(D) Above critical temperature and pressure

56.

O(1) PhMgBr(2) H O3

(A) Conc.H SO2 4 (B) HBrCCl4

(C) C H2 5OH (D) is OEt

Ph

Identify the type of mechanism(s) that take place in following reaction sequence (A to D).(A) Nucleophilic substitution (B) Nucleophilic addition(C) Electrophilic addition (D) Elimination


CHEMISTRY


57. A substance A reacts at 500 K by parallel reactions to give B and C as shown :

k ,E1 A1

k ,E2 A2

A

B

C

Reaction-1 : k = 10 sec . E =80 kcal/mole1–3 –1

A1

Reaction-2 : k = 10 sec . E =100 kcal/mole2–2 –1

A2

Identify the INCORRECT statement(s).(A) The net activation energy for conversion of A is 90 Kcal/mole.(B) The pre-exponential factor for 1st reaction is smaller as compared to 2nd reaction.(C) |H| for reaction-1 must be greater than reaction-2.(D) Fraction of A reacting by either of the reaction will be same.

58. Correct order(s) for molecular species(A) I – O bond length : IO2F2

– > IOF3 (B) Bond length : XeF2 > XeF4

(C) Bond length : XeO3 > IO3– (D) Bond length : XeO6

4– > XeO3






P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T


Pair of complexes Characteristics exhibited by pair of complexes

(A) [Fe(H2O)2(NH3)4]Br2, [NiBr(H2O)(en)2] NO3 (P) Strucural isomerism

(B) [Co(NO2)2(NH3)4]Cl, [Cd(SCN)2(H2O)2] (Q) Geometrical isomerism

(C) [Ir(NCS)2(Ox)2]3–, [Fe(CN)2(en)2] (R) Equal number of unpaired electrons

(D) [PtBrCl(H2O)4]Br2, [Rh(gly)3] (S) Minimum two space isomers are coloured

(T) Low spin complex



CHEMISTRY

60. 50 ml of 0.1 M ethylene diamine ( 1bK = 10–6 , 2bK = 10–9) solution is titrated with 0.1 M HCl (aq) solution

match the effect of addition.

Column I Column II(A) 25 mL of HCl (P) Buffer solution

(B) 50 mL of HCl (Q) pH > 7

(C) 75 mL of HCl (R) Multistep hydrolysis processes

(D) 100 mL of HCl (S) pH < 7

(T) First or second equilvalence point



CODE - ADATE : 26-07-15

B. Question paper format :9. The question paper consists of 3 parts (Mathematics, Physics and Chemistry). Each



11. Section II contains 2 groups of questions. Each question has 3 questions based ona paragraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out ofwhich only one of correct.

12. Section III contains 4 multiple choice questions. Each question has 4 choices (A),(B), (C) and (D) for its answer, out of which one or more is/are correct.

13. Section IV contains 2 questions. Each questions has four statements (A, B, C and D)given in Column I and five statements (P, Q, R, S and T) in Column II. Any givenstatement in Column I can have correct matching with one or more statement(s)given in Column II. For example, if for a given question, statement B matches with thestatements given in Q and R, then for that particular question, against statement B,darken the bubbles corresponding to Q and R in the ORS.

C. Marking Scheme :


15. For each question in Section II, you will be awarded 4 marks if you darken thebubble(s) corresponding to the correct choice(s) for the answer, and zero mark if nobubble is darkened. In all other cases, minus one (–1) mark will be awarded.

16. For each question in Section III, you will be awarded 4 marks if you darkened thebubble corresponding to the correct answer, and zero mark if no bubble is darkened.In all other cases, minus one (–1) mark will be awarded.

17. For each question in Section IV, you will be awarded 2 marks for each row inwhich you have darkened the bubble(s) corresponding to the correct answer. Thus,each question in this section carries a maximum of 8 marks. There is no negativemarking for incorrect answer(s) for this section.




















CODE - A


DATE : 26-07-15




1. The first term in a sequence of numbers is T1 = 5. Succeeding terms are defined by the statementTn – Tn–1 = 2n + 3 n 2. The value of T50 is.(A) 2700 (B) 2842 (C) 2900 (D) 2698

2. Let A and B be 3 × 3 symmetric matrices such that X = AB + BA and Y = AB – BA, then (XY)T is equal to[(XY)T is the transpose of matrix XY](A) XY (B) YX (C) –XY (D) – YX

3.

36

3

x2x

dx)1x( =

(A) 4x 2x + C (B) Cx

2x2

3

(C) C

xx2x

3

36

(D)

x2x3

+ C

where C is arbitrary constant.

4. The solution of the differential equation 2

dxdy

+ dxdy

(cosx + secx) + 1 = 0 is :

(A) y = sinx + C (B) y = cos x + C(C) y = – n |secx + tanx| + C (D) y = n |secx + tanx| + Cwhere C is arbitrary constant.



MATHEMATICS




5. A rod of fixed length 2 slides along the positive coordinate axes. If it meets the axes at A(a, 0) and B(0, b),

then the value 22

b1b

a1a

can be

(A) 7 (B) 8 (C) 9 (D) 10

6. Let })x{1(}x{2

})x{1(sin})x{1(cos)x(f1–1–

where {x} denotes the fractional part of x, then

(A) 4

)x(flim0x

(B) )x(flim2)x(flim

–0x0x

(C) 24)x(flim

–0x

(D)

22)x(flim

–0x


MATHEMATICS


7. If f : (0, 1) R is defined by f(x) =

n

n 1

2

2n 0

x

1– x

, then

(A) f–1(x) = x

x 1(B)

12

0

1f(x)dx ln2 –2

(C) 1

0

f(x)dx ln2 – 1 (D)

1

0

1 1 1f(x)dx .......2 3 4

8. If and are the roots of the equation ax2 + bx + c = 0 and = 3, where a, b, c are in A.P., then 2 + 2 =(A) 2 (B) –2 (C) 4 + 4 (D) +

9. Let f(x) = 2

2

(x – 2) 3 x 2

k x x 2

, then which of the following is/are true :

(A) f(x) is non differentiable for all real values of k.(B) The range of f(x) is [3, ) k [3, ).(C) f(x) has no local extrema at x = 2, then k –1.

(D) 3

2

11f(x)dx .3


MATHEMATICS





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

10. Column-I Column-II(A) If 2asinx – asin3x 6 x R then the number of non zero (P) 0integral value(s) of 'a' is(B) Tangents are drawn to x2 + y2 = 16 from the point P(0, h). (Q) 1These tangents meet the x-axis at A and B. If the area of triangle

PAB is minimum, then 8h2

=

(C) If 'k' denotes the number of ways in which 3 squares can be (R) 2related on chess board which lie on same diagonal line and liebelow the main diagonal and ''denotes the coefficientof x3 in (1 + x)3 + (1 + x)4 + (1+x)5 + (1 + x)6 + (1 + x)7,then k – is equal to(where the main diagonal on chess board is a diagonal alongwhich the north-west corner lie).

(D) Sum of all real solutions of equation 12

+ |sinx| = cosx in [0, 2] is k, (S) 3

then the value of k is (T) 4


MATHEMATICS



(A) If 2 3 100

x 0

1– (1– sinx)(1– sin2x) (1– sin3x) .....(1– sin100x)limx

(P) 3

= k (67670) then the value of k is(B) The number of solution of the equation cos sin + 6(cos – sin) + 6 = 0 (Q) 4

in [0, 30] is equal to.

(C) Let a circle of radius 23 is touching the lines x2 – 4xy + y2 = 0 in the first (R) 5

quadrant at points A and B. If area of triangle OAB ('O' being the origin) is ,then 2 equals

(D) If the value of the definite integral

2 /2

20 0

dx dxk ,(2 sin2x) 3 cos x

(S) 8

then the value of k is (T) 10


MATHEMATICS




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

12. If f (x) is a non decreasing function for which f (0) = 0, f(0) = 5 and f (x) – f (x) 0 x R, then the value

of 111

2

23

21

dx)x(f is equal to.

13. A natural number has four divisors and sum of its divisors excluding 1 and itself is 30, then the number ofsuch numbers is.



MATHEMATICS

14. Let f(x) = ex – x – 3x3

. The minimum value of f(x) is 'a' and this value occurs at x = b, then a + b =

15. If nlim

2222 n

1......31

21

11

= 6

2, then n

lim

33333333 )1n(n

1.....431

321

211

= 2k – 2 ,

then k is equal to

16. Area bounded by the straight lines x2y – y3 – x2 + 5y2 – 8y + 4 = 0 is equal to



MATHEMATICS17. If the equation of tangent drawn to curve y = f(x) at its point P(3, 5) is 5x – 4y + 5 = 0 and

3xlim )))x4(ncos(1(

)1)3.....331(23( 2192)x(f4

= 2 (a.320 nc)2

where a and c are prime numbers, find a + c.

18. Let f : [0, ) R be a continuous, strictly increasing function such that f3(x) = dt)t(ftx

0

2 . If a normal is

drawn to curve y = f(x) with gradient – 21

, then find the intercept made by it on y-axis.

19. Let n be the smallest positive integer larger than 150 so that the number nC151 is divisible by nC150 but is notequal to it. The last digit of n, is :


PART II : PHYSICSECTION - I


20. The charge flown from P to Q when the switch S is closed is

S

2 F

5V

P Q

3 F

(A) 3 C (B) 6 C (C) 9 C (D) 15 C

21. Two small rings O and O are put on two vertical stationary rods AB and AB, respectively. One end of aninextensible thread is tied at point A. The thread passes through ring O and its outer end is tied to ring O.Assuming that ring O moves donwards at a constant velocity v1, determine the velocity v2 of the ring O,when AOO = .

(A) 2

12sin / 2v

cos

(B)

2

12cos / 2v

sin

O

v1

BB

O

v2

A A

(C) 2

13cos / 2v

sin

(D) None of these



PHYSICS22. n number of water droplets, each of radius r, coalesce, to form a single drop of radius R. The rise in temperature

d is (T is surface tension, J is a constant, no energy is lost)

(A) 2TrJ (B)

3T 1 1J r R

(C) 3TJ

(D) 3T 1 1J r R

23. The efficiency of an ideal gas with adiabatic exponent '' for the shown cyclic process would be

v2v0

C

AB

T0 2T0 T

v0

(A) (2ln2 1)

/ ( 1)

(B) (1 2ln2)

/ ( 1)

(C) (2ln2 1)

/ ( 1)

(D) None of these



PHYSICS




24. An ellipsoidal cavity is carved within a perfect conductor. A positive charge q is placed at the centre of thecavity. The points A and B are any two points on the cavity surface. Then(A) Electric field near A in the cavity must be equal to the electric field near B in the cavity(B) Surface charge density at A must be equal to the surface charge density at B.(C) Potential at A must be equal to the potential at B(D) Total electric field flux through the surface of the cavity is q/0

25. Three identical plates of area A are arranged as shown. A charge +Q is given to plate (2). Then

d 2d

(1) (2) (3)

(A) Charge + 2Q/3 appears on plate 1 (B) Charge – 2Q/3 appears on plate 1(C) Charge – Q/3 appears on plate 3 (D) Charge on two faces of plate 2 are 2Q/3 and Q/3

26. If the tension in a string is changed by 21%, fundamental frequency of the string changes by 15 Hz. Whichof the following statements will also be correct?(A) Original fundamental frequency is about 150 Hz(B) Velocity of propagation changes by nearly 4.5%(C) Velocity of propagation changes by nearly 10%(D) Fundamental wavelength changes by nearly 10%


PHYSICS


27. An opaque sphere of radius R lies on a horizontal plane. A light source is placed above sphere as shown.Then

Light

R

(A) Area of shadow on the plane is 2R2

(B) Area of shadow on the plane is 3R2

(C) If the sphere is submerged in liquid, area of the shadow on plane decreases(D) None of the above

28. A cork suspended from the bottom of a container filled with water with a string as shown in the figure. If thecontainer accelerated in horizontal direction towards right, which is/are correct?

(A) Inclination of string with vertical is tan–1(a/g) towards left(B) Inclination of the string with vertical is tan–1(a/g) towards right(C) Inclination of the string with vertical is /2 – tan–1 (a/g) towards left(D) Magnitude of force of buoyancy on the ball remains same





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

29. Column I shows certain thermodynamic systems and column II represents thermodynamic properties.Column I Column II

(A) An ideal gas is filled in a cylindrical vessel of

Ideal Gas

Atmosphere

Hg

(P) Internal energy of thewhich is enclosed by a massless piston. gas is increasingMercury is filled above the piston as shown.Now gas is slowly supplied heat. Mercury doesnot spill. The system is kept in open atmosphere.

(B) A cylindrical vessel is enclosed by a light piston. The

IdealGas

Atmoshpere(Q) Pressure of the

piston is connected to ceiling by an ideal spring as gas is increasing.shown in figure. Spring is initially relaxed and thenheat is supplied slowly to the ideal gas in the vessel.The system is kept in open atmosphere.

(C) A thermally insulated cylindrical vessel is enclosed

IdealGas

Atmosphere (R) Temperature of theby a light thermally insulated piston. Some sand is gas is decreasing.kept on top of piston as shown in figure. The systemis kept in open atmosphere. Now sand grains areremoved slowly one by one.

(D) A good conducting cylindrical vessel is enclosed by

IdealGas

Atmosphere

(S) Work done bya light thermally insulated piston. Some sand is gas is positive.kept on top of piston as shown in figure. The systemis kept in open atmosphere. Now sand grains areadded slowly one by one.

(T) Molar heat capacity ofthe gas is finitely positive.


PHYSICS30. Two concentric metal shells of radii rA = 1 cm and rB = 2 cm

are given charges and action performed as shown.

AB

Column-I Column-II

(A) qA = 2 C, qB = 4C A grounded (P) Final 1qq

B

A

(B) qA = 4 C, qB = – 4 C B grounded (Q) Final B

Aqq

= 0

(C) qA = – 2 C, qB = 4 C (R) Final B

Aqq

< 1, non zero

A and B connected

(D) qA = – 1 C, qB = 2C (S) qA and qB do not change during the process

A grounded (T) Electric field between A and B is zero



PHYSICS




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

31. If each battery in figure has internal resistance of 1, what should be the e.m.f. of X (in V) for there to be nodeflection in the galvanometer ?

9V

X

5

3



PHYSICS32. A galvanometer (coil resistance 99 ) is converted into an ammeter using a shunt of 1and connected as

shown in the figure 1. The ammeter reads 3 A. The same galvanometer is converted into a voltmeter byconnecting a resistance of 101 in series. This voltmeter is connected as shown in figure 2. Its reading isfound to be 4/5 of the full scale reading.

12V

A

2

r

12V

V 2

r

Figure 1 Figure 2

Find the range of the ammeter (in ampere) (Give answer in nearest integer).

33. If a charge q (1 milli columb) is moving towards the centre of an earthed conducting sphere of radius 1m witha velocity 2 cm/s. Find the current (in A) flowing in the ammeter shown in figure when q is at a distance 2mfrom centre of sphere.

C AR

+q


34. A bent tube is lowered (to a very small depth) into water stream as shown in the figure. The velocity of thestream relative to the tube is equal to v = 2.5 m/s. The closed upper end of the tube located at a height of11.25 cm has a small orifice. If water spurt up to height 5x (in cm) from the orifice then find x.

h = 11.25 cm0

h

v

35. A ball is projected normally from point P (which is on an inclined plane) with speed u = 10 2 ms–1. It strikesthe vertical wall normally. If all the collisions are perfectly elastic, then find the time period (in sec) of periodicmotion.

uP

45°

Q


PHYSICS


36. A ray of light enters a spherical liquid drop (refractive index = 3 ) from air at an angle of incidence ( 0).

It suffers two internal reflections (not TIR) inside the drop and finally comes out of the drop. If ( 0) is suchthat the deviation of the ray with respect to its original direction is minimum, find the value of 12 sin2.

37. A convex lens of focal length f = 10 cm is cut through a dimeteral plane into two semicircular halves. In doingso, glass of 0.5 mm thickness is lost. The two halves are then joined together. This lens is placed symmetrically5 cm in front of a slit which is illuminated with light of wavelength = 5000 Å. A screen is placed on the otherside of the lens at a distance of 90 cm from the lens, perpendicular to the optical axis of the lens. Find totalnumber of bright fringes formed.

38. If the kinetic energy of pulse travelling in a taut string is 50x (in micro joule), find x.[Given T = 10N & = 0.1 kg/m].

1mm

10cm 5cm


PHYSICS


PART III : CHEMISTRYECTION - I


39. Which of the following reagents are used in Bayer's process for dissolution of Al2O3 and for precipitation ofAl(OH)3 respectively.(A) Fe2O3, SiO2 (B) NaOH, CO2 (C) NaOH, SiO2 (D) Fe2O3, CO2

40. If An be the area enclosed by nth orbit in H-atom, then correct statement(s) for the graph n(An) vs n(n), is(A) Passes through origin (B) Is a straight line of slope 4(C) Is a parabola (D) Is a circle

41. Observe the reaction given below:-

Br2

hCH OH(aq.)3 Solution "A"

Br2

FeCH OH(aq.)3 Solution "B"

Which of the above solution are acidic ?(A) A only (B) B only (C) A & B (D) None

42. Find rHº at 300 K for reaction 4 NH3(g) + 3O2(g) 2N2(g) + 6H2O()

Given : At 300 K, omS (H2O, ) = 70 J/K.mol ; o

mS (N2, g) = 192 J/K.mol ; omS (NH3, g) = 193 J/K.mol ;

omS (O2, g) = 205 J/K.mol ; o

fG (H2O, ) = 237 kJ/mol ; fGº (NH3, g) = 16.5 kJ/mol

(A) 1181.1 kJ/mol (B) 1530.9 kJ/mol (C) –173544 kJ/mol (D) 174.9 kJ/mol





43. Which of the following statement(s) is/are TRUE about the transition metal alkene complexes(A) Back bonding weakens the double bond of the alkene(B) Back bonding strengthen metal-alkene interaction(C) Electron withdrawing subtitutents present on alkene reduce back bonding(D) CO-ligand(s) present around central metal strengthen metal-alkene interaction

44. Which of the following will form a significant meta substituted major product during the reaction (if any)

(1)

NO2

Cl + AlCl3(2)

NH3

Cl + AlCl3

O

(3) N Cl , Al2

(4) Br2

OCH=CH2

Fe

(A) 1,2,3,4 (B) 1,2,3 (C) 3,4 (D) 3



CHEMISTRY


45.

OOCH3

NaOH, A

(major)

Br , CCl2 4 Solution (B)

Correct statement(s) about the solution B is/are :-(A) It has 2 products (B) It has 1 product(C) It is optically Inactive mixture (D) It is optically active mixture

46. Assume the complex [Ni(PPh3)2(SCN)2] is paramagnetic. The analogous complex of Pd(II) is diamagnetic.The isomerism shown by Pd(II) complex is/are(A) Linkage (B) Optical (C) Geometrical (D) Polymerization

47. Given : o2Fe |Fe

E = – 0.44 V ; o3Cr |Cr

E = – 0.74 V

o2Hg |Hg

E = + 0.086 V ; oCl |Cl¯2

E = + 1.36 V

then cell reaction(s), which can be non-spontaneous is/are -

(A) Hg(l) + Fe2+(aq) Hg2+(aq) + Fe(s) (B) Cr3+(aq) + 3Cl–(aq) Cr(s) + 2Cl23

(g)

(C) 3.Hg(l) + 2.Cr3+(aq) 3.Hg2+(aq) + 2Cr(s) (D) Fe(s) + Cl2(g) Fe2+(aq) + 2Cl–(aq)


CHEMISTRY





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

48. Match the reaction gives to the intermediate formed & mechanism involved.Column-I Column-II

(A)

CH3

NBSBenzoyl proxide

(P) SN1

(B) OH O3

(Q) Free radical intermediate

(C)HClH O2

(R) Carbocation intermediate

(D)

F

NO2

KOH (S) Carbanion intermediate

(T) Nucleophilic aromatic substitution


CHEMISTRY


49. Column- I (species) Column-II (Related Properties)

(A) F2 (I), Cl2 (II) (P)

I II

Ener

gy

r

(B) N2 (I), N2

– (II) (Q)

III

Ener

gy

r

(C) O2 (I), B2 (II) (R) Number of electrons in bonding M.O. (I) = (II)(D) H2 (I), Li2 (II) (S) Bond order of (I) = (II)

(T) Number of electron in HOMO in (I) = (II)


CHEMISTRY




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

50. A real gas is subjected to an adiabatic process causing a change in state from (3 bar, 50 L, 500 K) to(4 bar, 40 L , 600 K) against a constant pressure of 4 bar. Calculate magnitude of enthalpy change (in kJ) forthe process.

51.

O Me

CH3

+

O Me

CH3

(1) CH MgBr(excess)3

(2) H O3

Number of optically active products in the reaction are :-


CHEMISTRY52. If magnitude of resonance energy of CH3COOH(g) is x then from the following thermodynamic data at 300K,

calculate the value of x

25 (in kJ/mol)

CH3COOH(l) CH4(g) + CO2(g) , Hr = 25 kJ/moleResonance energy of CO2(g) = –25 kJ/mol ; Hvap(CH3COOH, ) = 50 kJ/molBond enthalpy : C – H = 400 kJ/mole ; C – O = 350 kJ/mole ; O = O = 500 kJ/mole;C – C = 350 kJ/mole; O – H = 450 kJ/mole; C = O = 800 kJ/mole; H – H = 400 kJ/mole.

53. Given that crystal field stabilization energy for [Co(H2O)6]2+ is 7200 cm–1 , pairing energy for Co2+ is

20,800 cm–1, then calculate the value of 30

10

in cm–1.

54. If lattice enthalpy of KCl(s) is x kJ/mol then calculate the value of x

100 .

Given : fHº(KCl, s) = –436 kJ/mol ; Hºhydration (K+, g) = –321 kJ/molHºhydration (Cl–, g) = –362 kJ/mol ; fHº (K+, aq) = –252 kJ/mol

fHº(Cl–, aq) = –167 kJ/mol




CHEMISTRY55. How many of the following reactions will prefer following a path way which gives 1st order kinetics.

(a) OH

H+

(b)

Cl

Cl

NaNH2

(c) NO2

CH –CH –F2 2

EtO /EtOH– CH=CH2

NO2

(d)

SH

Cl

KOH

S (e) Cl

NaICl

(Acetone)

(f) Cl

H O2

OH(g) N

Base,

(h) O

(1) PhMgBr(2) H+


56. For 2A(g) B(g) + C(g) , following graph is ptotted :

(3.33 × 10 )–3

ln Keq

T1

If = 45º , then calculate value of Keq. at 300 K.

57. At what pH, the oxidation potential of hydrogen gas electrode is 0.27 V.

[Given : Pressure of H2(g) = 0.1 bar ; 06.0F

RT303.2 ]

CHEMISTRY




CODE - A




11. Section II contains 5 multiple choice questions. Each question has 4 choices (A),(B), (C) and (D) for its answer, out of which one or more is/are correct.

12. Section III contains 2 questions. Each question has four statements (A, B, C and D)given in Column I and five statements (P, Q, R, S and T) in Column II. Any givenstatement in Column I can have correct matching with one or more statement(s)given in Column II. For example, if for a given question, statement B matches with thestatements given in Q and R, then for that particular question, against statement B,darken the bubbles corresponding to Q and R in the ORS.

13. Section IV contains 8 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9. The answer will have to be appropriately bubbled inthe ORS as per the instructions given at the beginning of the section.

C. Marking Scheme :


15. For each question in Section II, you will be awarded 4 marks if you darken thebubble(s) corresponding to the correct choice(s) for the answer, and zero mark if nobubble is darkened. In all other cases, minus one (–1) mark will be awarded.


17. For each question in Section IV, you will be awarded 4 marks if you darken thebubble corresponding to the correct answer, and zero mark if no bubble is darkened.In all other cases, minus one (–1) mark will be awarded.

DATE : 26-07-15




















CODE - A


DATE : 16-08-15




1. If 214x

and 2

2

12–2y

where is a real parameter. If maximum and minimum values of x2 – xy + y2

are M and m respectively, then arithmatic mean of M and m be(A) 4 (B) 6 (C) 8 (D) 1

2. If 2

......!4

–!2

1–cot......!7

–!5!3

––tan42

1–753

1–

then maximum value of

equals to

(A) 21– (B) 1 (C)

21

(D) 21

3. The area bounded by the curve f(x) = ||tan x + cot x| – |tan x – cot x|| between the lines x = 0, x = 2

and

x-axis is

(A) ln 4 (B) 2ln (C) 2ln2 (D) None of these

4. The equation of normal to the circle (x – 1)2 + (y – 2)2 = 4 which is at a maximum perpendicular distance fromthe point (–1, –1) is(A) x + 2y = 5 (B) 2x + y = 4 (C) 3x + 2y = 7 (D) 2x + 3y = 8



MATHEMATICS


5. The index of the Nilpotency of the matrix

3–1–2–625311

is

(A) 2 (B) 3 (C) 4 (D) None of there

6. A bag contains tickets numbered 1 to 25. Five tickets are drawn at random and arranged in ascending order.The probability that 2nd and 4th bear the numbers 12 and 18 respectively is

(A) 1

138 (B) 1151

(C) 2301

(D) None of these

7. If

5723

A

12–11–

=

401–2

, then trace of A is equal to

(A) – 25 (B) – 21 (C) – 15 (D) – 11

8. If y =

xcos1aa

xsintan1a

2

1a

x2

122

where ,11,a then y’

2 equals

(A) a1

(B) a2

(C) a21

(D) a


MATHEMATICS





Let A, B, C are real numbers so that A + B + C = 15 and AB + BC + CA = 27 then

9. Minimum possible value of the product (ABC).

(A) –49 (B) –743 (C) –243 (D) 0

10. Maximum possible value of the product (ABC).

(A) 13 (B) 17 (C) 19 (D) 31


MATHEMATICS


Paragraph for Question Nos. 11 to 13A shoping mall is running a scheme. Each packet of detergent 'SURF' contains a coupon which bears a letterof the word 'SURF'. If a person buys at least four such packets and produce all the letters of the word 'SURF',he gets one free packet of detergent 'SURF'.

11. If a person buys 8 such packets at a time, then the number of different combination of coupon he has(A) 120 (B) 165 (C) 145 (D) None of there

12. If a person buys 8 such packets at a time, then the probability he gets exactly one free packet

(A) 12035

(B) 16534

(C) 14536

(D) 15033

13. In above question the probability he gets exactly two free packets

(A) 1201

(B) 1651

(C) 1451

(D) 1501


MATHEMATICS




14. If P and Q are symmetric non singular matrices and PQ = QP, then which of the following is/are true.(A) QP–1 = P–1Q (B) PQ is skew symmetric(C) P–1Q is symmetric (D) PQ is symmetric

15. Let fn() =

n

0n

n4n .2sin

41

Then which of the following alternative(s) is/are correct?

(A) f2 21

4

(B) 422

8f3

(C) f4 12

3

(D) f5() = 0

16. If 0 and ,sin–1–sin12

sin

then possible values of tan , is

(A) 4/3 (B) 0 (C) –3/4 (D) –4 / 3


MATHEMATICS


17. A certain coin lands head with probability p. Let Q denote the probability that when the coin is tossed fourtimes the number of heads obtained is even. Then

(A) There is no value of p, if Q = 1/4

(B) There is exactly one value of p if Q = 3/4

(C) There are exactly two values of p if Q = 3/5

(D) There are exactly four values of p if Q = 4/5

18. Which of the following sets can be the subset of the general solution of the equation1 + cos 3x = 2 cos 2x ?

(A) 3/n (B) 6/n (C) 6/n (D) 2nwhere n I


MATHEMATICS



This section contains 10 questions. The answer to each of the questions is a single-digit integer, rangingfrom 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened.For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively,then the correct darkening of bubbles will look like the following :In all cases round answer to nearest integer value (if required)

0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

19. A pack of playing cards was found to contain only 51 cards. If the first 13 cards which are examined are allblack. If P is the probability that the missed one is red. Then the value of 3P is ____________

20. Let the matrix A =

122212221

be a zero divisor of the polynomial f(x) = x2 – 4x – 5.

Find the unit digit of the sum of all the elements in the matrix A3.


MATHEMATICS


21. Let Dnf

Cn5

Bn

An

1r21r2r 23n

1r

4

ND,C,B,A

where f(n) is the ratio of two linear polynomials such that nLim f(n) =

21

Find the value of DCBA where [.] denotes greatest integer function.

22. Consider the circle W x2 + y2 = 81. Let AB be a diameter of circle W. AB is extended through A to C. PointT lies on W so that line CT is tangent to W. Point P is the foot of the perpendicular from A to the line CT.

Find the unit digit of the maximum value of (BP)2.

23. Given y(0) = 2000 and dxdy

= 32000 – 20y2, then find the value of xLim y(x)

10 .


24. A pair of students is selected at random from a probability class. The probability that the pair selected will

consist of one male and one female student is 1910

. Find the sum of the digits of the maximum number of

students the class can contain.

25. For any integer n 2 and two n × n matrices with real entries A, B that satisfy the equation A–1+ B–1=(A+B)–1.If det(A) = 4, find the value of det (B).

26. Given that 2dx

2xcos.....

8xcos

4xcos

2xcoslim

01–nn

then the value of

dxx

xsin

0

3

. Find .

MATHEMATICS



27. In an organisation number of women are times that of men. If things are to be distributed among them

than the probability that the number of thing received by men are odd is 1

21–

21

. Find .

28. Find the number of all real solution(s) (x, y) of the equation 16x4 + y4 + 8x2 + 2y2 – 24xy + 8 = 0.

MATHEMATICS





29. Position of object O and screen is fixed and lens is moved. At two positions of lens we get clear image on thescreen. First position is at 30 cm from object and second positiion is at 50 cm from object. Find focal lengthof lens.

(A) 254

(B) 754

(C) 454

(D) 654

30. In a YDSE apparatus, d = 2 mm, = 600 nm, D = 1 m. The slits individually produce same intensity on the

screen. Find the position (distance from central maximum) of point where intensity is 34

times of the

maximum intensity on screen.(A) 0.01 mm (B) 13 × 10–4 mm (C) 0.05 mm (D) 1.5 × 10–4 mm



PHYSICS


31. A cubical vessel of edge 1 m and total thermal resistances (of its walls) is 1R

(where, R is universal gas

constant) has a small hole in one of its walls. It is kept in a very big closed chamber whose temperature T0

remains constant. In the chamber and vessel, a monoatomic gas is filled at a same constant pressure P0. Attime t = 0, temperature of the gas in the vessel is T1 (< 2T0/3). When temperature of the gas in the vesselbecomes 0.8 T0, rate of change of moles in it will be

(A) 1

10 (B) 16 (C)

110

(D) 16

32. When a thin transparent sheet of refractive index 32

is placed near one of the slits in Young's double slit

experiment, the intensity at the centre of the screen reduces to half of the maximum intensity. The minimumthickness of the sheet should be

(A) 4

(B) 8

(C) 2

(D) 3

33. A ray of light is incident at an angle of 60º on one face of a prism of angle 30º. The emergent ray isperpendicular to the other face. The angle of deviation is :(A) 60º (B) 0º (C) 30º (D) 90º


PHYSICS


34. A and B are two concentric spheres. If A is given a charge Q while B is earthed as shown in figure,

(A) the charge density of A and B are same (B) the field inside and everywhere outside A is zero(C) the field between A and B is not zero (D) the field inside and outside B is zero

35. A polished metal plate with rough black spot on it is heated to about 1400 K and quickly taken to dark room.Which one of the following statements is true ?(A) Spot will appear brighter than plate (B) Spot will appear darker than plate(C) Spot and plate will be equally bright (D) Spot and plate will not be visible in dark

36. Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. the phase

difference between the beams is 2

at point A and at point B. Then the difference between the resultant

intensities at A and B is(A) 2I (B) 4I (C) 5I (D) 7I


PHYSICS




Paragraph for Question Nos. 37 to 38A long rectangular slab of transparent medium of thickness d is placed on table with length parallel to x-axisand width parallel to the y-axis. A ray of light traveling along y-axis at origin. The refractive index of the

medium varies as x/d1 e . The refractive index of the air is 1.

37. Determine the x-coordinate of the point A, where the ray intersect the upper surface of the slab air boundary.

(A) d(ln2) (B) 2d (ln2) (C) d(ln2)

2(D) None of these

38. Write down the refractive index of the medium at A

(A) 5 (B) 5 (C) 7 (D) 8


PHYSICS


Paragraph for Question Nos. 39 to 41Analyse the given circuit in the steady state condition. Charge on the capacitor is q0 = 16 C.

39. Find the current in 2 resistance

(A) 24 A9 (B)

20 A9 (C)

22 A9 (D) None of these

40. Find the emf of the battery(A) 20V (B) 24V (C) 22V (D) 8V

41. If now the battery is removed and the points A and C are shorted. Find the time (in micro-second) duringwhich charge on the capacitor becomes 8 C.(A) 12 (ln2) (B) 9 (ln2) (C) 16 (ln2) (D) None of these





42. A light source is submerged inside water. It is moving in upward direction due to buoyancy force. Which ofthe following is INCORRECT?(A) Percentage of light transfering from water to air is increasing.(B) Percentage of light transfering from water to air is constant(C) Base area of light cone is increasing(D) Base area of light cone is decreasing

43. In the arrangement shown in figure, vessel is thermally insulated. An ideal gas is filled in the cylinder havingpressure P greater than atmospheric pressure P0. The spring of force constant K is initially unstreteched.The piston of mass m and area s is frictionless. In equilibrium, the piston rises up a distance x0, then

(A) Final pressure of the gas is 00

Kx mgPs s

(B) Work done by the gas is 20 0

1Kx mgx2

K

m,s

P

P0

(C) Decrease in internal energy of the gas is 20 0 0 0

1Kx mgx P sx2

(D) Temperature of the gas increases

44. A string fixed at both ends is vibrating as shown in figure, then mark correct statements

A Bx y

(A) All particles in between x and y are vibrating in phase(B) All particles in between A and x are vibrating in phase with particles between x and y(C) All particles between A and X are vibrating in phase with particles in Y and B(D) All particles of string are in phase



PHYSICS45. Two cylinders A and B of equal capacity are connected to each other via a stop cock. A contains a gas at

standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. Ifthe stop cock is suddenly opened then(A) Final pressure of gas in A and B is 0.5 atm(B) There is no change in internal energy of the system(C) The intermediate states of the system (before setting to the final equilibrium state) are well defined(D) Through out the process, temperature remains constant.

46. Figure shows a potentiometer circuit. The length of potentiometer wire is L and its resistance is 2R. Neglectthe internal resistance of the cells. Select the correct alternative

(A) When only S1 is closed, 1

L 6

L

R 2R

GS2

S1No deflection

R3V

1V

(B) When only S2 is closed, 1

L 2

(C) When both S1 and S2 are closed, 1

L 6

(D) When both S1 and S2 are closed, 1

L 2


PHYSICS



This section contains 10 questions. The answer to each of the questions is a single-digit integer, rangingfrom 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened.For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively,then the correct darkening of bubbles will look like the following :In all cases round answer to nearest integer value (if required)

0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

47. In a circuit shown in figure if the internal resistance of the sources is negligible, at what value of resistance R(in ohm) will the thermal power generated in it will be the maximum ?

6v

10vR

3

6


PHYSICS


48. In a region an electric field E = 15 N/C making an angle of 30° with the horizontal plane is present. A ballhaving charge 2C, mass 3 kg and coefficient of restitution with ground 1/2 is projected at an angle of 30° withthe horizontal from the ground in the direction of electric field with speed 20 m/s. Find the time (in sec) afterprojection when ball hits the ground second time.

30°

E

ground

49. In the circuit shown, a time varying voltage V = (2000t) Volt is applied where t is in second. At time t = 5 ms,

determine the current I (R = 4 and capacitance C = 300 F). If this current is 30 x

10

amp. Find x

+–V R C

I


50. Determine the acceleration of 4 kg block (in m/s2) in the system shown in figure assuming that pulleys andstrings are ideal. (g = 10 m/s2). Round your ans. to nearest integer if required

8 kg2 kg

4 kg

51. A solid sphere of mass m and radius R initially rotating about its centroidal axis with 0 is gently placed onrough inclined plane with its axis horizontal as shown in figure. The angle of inclination of plane is . Find the

time after which sphere starts pure rolling.If this time is 0

0R

t xg(7 cos 2sin )

, find x . (Coefficient of

friction = ).

0

PHYSICS



52. A cube floating in a liquid contained in a beaker has one-third of its volume submerged in mercury. Water ispoured into the beaker till the cube is completely covered. What fraction of the volume of the cube is now

submerged in mercury? If the fraction is 1x

, find x. The relative density of mercury = 9.

53. The figure shows a RC circuit with a parallel plate capacitor. Before switching on the circuit, plate A of thecapacitor has a charge – Q0 while plate B has no net charge. Now, at t = 0, the circuit is switched on. Howmuch time (in second) will elapse before the net charge on plate A becomes zero.

(Given capacitance C = 1F, Q0 = 1mC, = 1000 V and R = 62 10

ln3

)

A B

SR

PHYSICS



54. A concealed circuit (a black box) consisting of resistors has four terminals. If a voltage is applied betweenclamps 1 and 2 when clamps 3 and 4 are open, the power liberated is P1 = 4W and when clamps 3 and 4 areclosed, the power liberated is P2 = 8W. If the same source is connected to the clamps 3 and 4, the powerliberated in the circuit when clamps 1 and 2 are open is P3 = 2W. Determine the power P4 consumed in thecircuit when the clamps 1 and 2 are connected and the same voltage is applied between the clamps 3 and 4.

R1 R2

R3

1

2

3

4

55. A transverse wave is passing through a string shown in figure. Mass density of the string is 1 kg/m3 and crosssection area of string is 0.01 m2. Equation of wave in string is y = 2sin (20t – 10x). Find the hanging mass (ingm). (t is time in sec. and x is position in m)

m

x

56. A convex lens of focal length 1.5 m is placed in a system of coordinate axis such that its optical centre is atorigin and principal axis coinciding with the x-axis. An object and a plane mirror are arranged on the principalaxis as shown in figure. Find the value of d (in m) so that y-coordinate of image (after refraction and reflection)is 0.3 m. (Take tan = 0.3)

(0,0)

d

(– 2, 0.1)0.1

2m

PHYSICS





57. Select correct pair of complexes that exhibit same type of isomerism.(A) [CoBr(NH3)5]Cl2 , [IrBr3(H2O)3] (B) [Cr(NO2)2(en)2]

+ , [Rh(SCN)(H2O)(ox)2]2–

(C) [Pt(gly)(NH3)(H2O)]+ , [Zn(gly)(NH3)2]+ (D) [CoCl2(NH3)4]

+, [CrBr(H2O)5]Br2

58. Which of the following processes causes the emission of an X-ray?(A) Alpha emission (B) Gamma emission (C) Positron emission (D) Electron capture

59. Compare rate of nucleophilic addition reaction

O

(a)

O

(b)CH – C – H3

O

(c)

(A) a > b > c (B) b > a > c (C) c > a > b (D) c > b > a

60. For the reaction A B, the activation energy of reverse reaction is twice that of forward reaction.If enthalpy of reaction is –90 kJ/mol, the activation energy of the reverse reaction is:(A) 60 kJ/mol (B) 45 kJ/mol (C) 180 kJ/mol (D) None of these



CHEMISTRY


61. Correct order of bond angle is

(A) 3 3CH CF

(B) 3–3 CHCH (C) CH4 > CF4 (D) 4 3CH CH

62.A

Br2

CCl4Cold KMnO4

Meso-2,3-dibromobutane

Product obtained are ?

(A) Position isomer (B) Diastereomers (C) Enantiomers (D) Identical

63. Calculate acid dissociation constant for the reaction H2O2 (aq) H+ (aq) + HO2– (aq).

Given : H2O2 (aq)+ 2H+(aq) + 2e– 2H2O (l) ; E° = 1.77 VHO2

– (aq) + H2O (l) + 2e– 3OH– (aq) ; E° = 0.87 VKw = 10–14 ; 2.303 × R × T = 5790 J/mol

(A) 10–30 (B) 10–16 (C) 10–12 (D) 10–6

64. Pair of complexes, which do not have equal number of unpaired electron(s).(A) [Co(CO)4]

–, [Ni(CN)4]4– (B) [Co(H2O)6]

3+, [NiF6]2–

(C) [Ni(en)3]2+[Cr(CN)6]

4– (D) [Co(CN)6]4–, [Cr(NH3)6]

3+



Comprehension TypeThis section contains 2 paragraphs. Based upon the first paragraph, 2 multiple choice questions and basedupon the second paragraph 3 multiple choice questions have to be answered. Each of these questions hasfour choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Question Nos. 65 to 66Organomagnesium halides were discovered by the French chemist Victor Grignard in 1900. Grignard receivedthe Nobel Prize for his discovery in 1912, and organomagnesium halides are now called Grignard reagents inhis honor. Grignard reagents have great use in organic synthesis.Grignard reagents are prepared by the reaction of an organic halide with magnesium metal in an anhydrousether solvent :

RX + Mg Et O2 RMgX

ArX + Mg Et O2 ArMgXGrignardreagents

65. Which of the following reaction form primary alcohol in major product.

(A)

MgBr

+

OEt O2

H O3

(B)

MgBr

+O Et O2

H O3

(C)

MgBr

+O Et O2

H O3

(D) O

HOMeMgBr

66. The Major product(A) of the following reaction is

Br

(i) Mg, Et O2

(ii) O

OMe(iii) NH Cl, H O4 2

A

(A) Me

OH

(B)

OH

MeMe

(C) C

O

(D)

OHPh

Ph



Refining of metal is very important stage of metallurgy. Refining of a metal depends on its nature andimpurities associated with it. Physical and chemical methods are used for refining prior to electrolyticrefining.

67. Which of the following metal is not refined by fractional distillation.(A) Zn (B) Cd (C) Hg (D) Sn

68. Which of the following statement is not correct about refining of metal by oxidation using air / oxygen.(A) Oxidation of an impurity is exothermic process(B) Haematite (Fe2O3) can remove impurity of manganese from iron in the presence of silica(C) Impurity of lead can be removed from silver by air oxidation(D) Impurity of iron can be removed from tin by air oxidation

69. Which of the following thermal decomposition reaction is not used for refining of respective element.

(A) Ni(CO)4 Ni + 4CO(g) (B) 2BI3 2B + 3I2

(C) TiI4 Ti + 2I2 (D) CuI2 Cu + 2I2



CHEMISTRY




70. Correct order(s) for following structures is/are

N NO

OO x1

x2

N

OO

x3

(A) x2 > x1 (B) > (C) > (D) x2 > x3

71. The energy of separation of an electron is 13.6 eV present in an orbit of He+. Which is incorrect statement(s)

(A) Orbit angular momentum of electron is h (B) Velocity of electron is 2.18 × 2 × 106 m sec–1.

(C) Kinetic energy of electron is –13.6 eV. (D) Potential energy of electron is –13.6 eV.

72.

F

NO2

NO2NH –NH2 2 A

O

H , + BProducts

Correct statements regarding above reaction is(A) Product A is 2, 4-DNP(B) A to B dehydration reaction(C) A to B, geometrical isomersm will obtained as a product(D) B is known as oxime


CHEMISTRY


73. Which is/are correct statement about refining of copper ?Given impure copper contains impurity of Fe, Ag and Au.EºAg+|Ag = 0.799 V ; EºFe+2|Fe = –0.44 V ; EºAu+3|Au = 1.50 V ; EºCu+2|Cu = 0.34 V(A) Ag and Au remains in anode mud.(B) Fe, Ag, Au remains in anode mud.(C) Blue colour intensity of CuSO4 remains constant during electrolysis.(D) O2(g) is evolved at anode

74. In which of reactions final product is ketone :

(A) CH3 – C C–H 2NaNH (a) –CH3 (b) 42

4

SOH

HgSO (c)

(B) H – C C – H 2NaNH (c) –CH–CH 23 (d) –4

22

HO,NaBH

OH,)OAc(Hg (e)

(C) R – C – OH||O

NaOH (a) I–3CH (b)

(D) 1-butyne 2NaNH (a) I–3CH (b) HO/2O2H)2(

THF:3BH)1(

(c)




Integer Answer TypeThis section contains 10 questions. The answer to each of the questions is a single-digit integer, rangingfrom 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened.For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively,then the correct darkening of bubbles will look like the following :In all cases round answer to nearest integer value (if required)

0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

75. x = number of reaction in which final product is aldehyde

(a) Ph – C N DIBAL–H–78ºC, H O2

(b) Ph – C N LiAlH4

(c)

O

ClPh

H2

Pd-BaSO4(d) Ph – C – O – Et

O

DIBAL–H

(e) O

OHPh

DIBAL–H (f) CH3 – CHCl2 aq. KOH

76. Calculate DSuniverse for phase change Na(s) ¾® Na() at 98ºC.(Given : Sm (Na, s) = 51 J/kmol ; Sm (Na, ) = 57.5 J/kmol

DfH (Na, ) = 2.4115 kJ/mol ; DfH (Na, s) = 0Assume all data provided at 98ºC.



CHEMISTRY

77. HO – Si – OH

R

R

n O2H3– Cyclic silicone,

Then find the value of expression |x – n| where, x = total number of Si – C bonds in Cyclic silicone.

78. Molar conductivities at infinite dilution of NaCl, HCl and CH3COONa are 130, 380 and 90 –1 cm2 mol–1 respec-tively if conductivity of 1.25 × 10–3 M CH3COOH is 3.4 × 10–5 –1 cm–1.Calculate pH of 1.25 × 10–3 M aq. solution of CH3COOH at 298 K.

79. Number of carbonyl compound with molecular formula C5H10O which give racemic mixture of secondaryalcohol with CH3MgBr forward with hydrolysis. (Including stereo)


80. A solution containg 0.2 mol of CH3NH2 (pKb = 4.0) is mixed with another solution containg 0.2 mol of HCl and2 litre solution formed at temp. TK. Calculate pOH of final solution at TK. [Given : pKw at TK = 13]

81. x = Number of compound, which undergo stable hydrate formation.

O

O

O

Ninhydrin

, Cl – C – H3C

O

(Chloral) ,

O

O

, O


CHEMISTRY


82. Given : C2H2(g) + H2(g) C2H4(g) + 175 kJfHº(C2H4, g) = 50 kJ mol–1 , fHº(H2O, g) = –240 kJ mol–1 ,fHº(CO2, g) = –390 kJ mol–1 , vapH(H2O, ) = 40 kJ mol–1 ,

Calculate the value of z.

Where comb 2 2| H (C H ) |z

257

83. For following metals find the value of expression |X + Y|Ag , Zn , Mn , Cu , Hg , Sn , Pb , Cr , Auwhere X = Number of metal(s) commercially extracted by metal displacement method.

Y = Number of metal(s) refined by poling.


CHEMISTRY


84. How many of titration curve are correctly matched ?

(i) Strong acid (HCl) v/s weak base (NH4OH)

7

pH

Volume of NH OH4

(ii) Strong base (NaOH) v/s NH4Cl

Volume of NH Cl4

solution

(iii) Weak acid (HCN) v/s strong base

Volume of NaOH

pOH

7

(iv) Strong acid (HCl) v/s weak base NH4OH

Volume of NH OH4

solution

(v) HCl v/s NaOH

Volume of NaOH

pH7

(vi) Weakacid v/s weak base

Volume of CH COOH3

solution

CHEMISTRY



CODE - ADATE : 16-08-15







C. Marking Scheme :
























CODE - A


DATE : 16-08-15




1. If , ,2

and < , then which one of the following is true

(A) cos –cose

(B) cos –cose

(C) cos –cose

(D)

cos –cose

2. Let f(x) = 2x3 – 3(2 + p)x2 + 12px + n(16 – p2) has exactly one local maxima and one local minima, Thennumber of integral values of p is :(A) 4 (B) 5 (C) 6 (D) 7

3. A student has managed to enter in Harward university. It was informed that probability of getting a scholarshipis 40%. In case of getting it, the probability of completing the course is 0.8, while in the case of not gettingthe schlolarship, the probability is only 0.4. If after some years from now, you meet the student completinghis course from harward, the probability that he was given the scholarship is :

(A) 8

17(B)

47

(C) 8

15 (D) 49



MATHEMATICS


4. In a table tennis single, two players play and one of them must win. Probability that A beats B is p, B beatsC is q and C beats A is r. If B plays with C and then the winner plays with A, then the probability that A will bethe final winner is :(A) qp + (1 – q) r (B) (1 – r) q + pq (C) pq + (1 – q) (1 – r) (D) qp + (1 – r)

5. The solution of the differential equation 0dxdy)e–x()y1( ytan2 1–

is

(A) 2x y1tane

= ytan2 1–e + c (B) cexe ytan2ytan2 1–1–

(C) cytanxe 1–ytan 1– (D) ytan 1–

ce2–x

(where c is an arbitrary constant)

6. Let A =

1 0 –10 2 21 1 3

. If B = adj A, C = AA–1 and N = | adj B |

| C | ,

then the number of ways in which N can be resolved as product of two divisors which are relatively prime is(A) 2 (B) 3 (C) 4 (D) 5


MATHEMATICS




Paragraph for Question Nos. 7 to 9Let f be a real valued function on R defined by f(x) = xe–x. Suppose a line parallel to the x-axis has distinctintersection points P,Q with the curve y = f(x). Denote the length of the line segment PQ equal to L. Also isthe value of x for which y = f(x) has a local maximum and R be the intersection point of the linex = and the line PQ.

7. If p and q are the abscissa's of the point P and Q respectively, then the ordered pair (p, q) is :

(A) L

L LL e,

e – 1 e – 1

(B) L

L LL Le,

e – 1 e 1

(C) L

L Le L,

e – 1 e – 1

(D) L

L LL Le,

e – 1 e – 1

8. If denotes the x-coordinate of the point of inflection, then ( – ) equals :(A) e – 1 (B) 1 (C) 2 (D) e – 2

9. Which one of the following relation hold good.(A) PR > RQ(B) PR = RQ(C) PR < PQ(D) Inequality between PR and RQ depends upon the distance between the line PQ and x-axis.


MATHEMATICS


Paragraph for Question Nos. 10 to 12Let A be the 2 × 2 matrices given by A = [aij] where aij {0, 1, 2, 3, 4}. Such that a11 + a12+ a21 + a22 = 4

10. The number of matrices A such that A is invertible are :(A) 18 (B) 19 (C) 20 (D) 12

11. The absolute value of difference between maximum value and minimum value of det(A) is equal to :(A) 4 (B) 6 (C) 8 (D) 5

12. The number of matrices A such that A is either symmetric or skew symmetric or both and det (A) is divisibleby 2 are :(A) 3 (B) 5 (C) 7 (D) 9


MATHEMATICS





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

13. Column-I Column-II(A) Let f(x) be a non constant polynomial (P) 5

Function and g(x) = |x3(x – 1) (x – 2) (x – 4) f(x)|.If g(x) is differentiable x R, then minimum number ofdistinct roots of f(x) is.

(B)

1tan2 n

n

nlimn – 1

(Q) 4

(C) For a > 0, let F : [–4a, 4a] R be an even (R) 3function such that f(x) = f(4a – x) x [2a, 4a]

and h 0

f(2a h) – f(2a)lim 4,h

then

h 0

f(h – 2a) – f(–2a)lim2h

(S) 2

(D) Let f(x) = x2 + ax + 3 and g(x) = x + b, where h(x) = 2n

2nn

f(x) x g(x)lim .1 x

If h(x) is continuous at x = 1 and x = –1, then a + b = (T) 1


MATHEMATICS


14. Consider f(x) = 1

0

t | t – x |dt, then

Column-I Column-II

(A) x Rmin f(x)

is equal to (P)13

(B)x [0,1]max

f(x) is equal to (Q)12

(C)x 1min

f(x) is equal to (R)1–2

(D) f(x) > 0 at x = (S)16

(T)1 11–3 2



MATHEMATICSSECTION - IV


0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

15. A semicircle is drawn outwardly on chord AB of the circle with centre 'O' and unit radius. The perpendicular

from O to AB meets the semicircle at C. The length of AB so that OC has maximum length is k , then k is

equal to :

16. The differential equation (xy3(1 + cosx) – y) dx + xdy = 0 represents the curves

2

2x

ay = bx3 + x2sinx + cxcosx – dsinx + k, a, b, c, d are constants (where k is arbitrary constant),

then a + b + c + d =



MATHEMATICS17. If f(x) is twice differentiable function for x [0, ] such that f(0) = f() = 0 and

/2

0

f(2x) f "(2x) sin x

cosxdx = k, then k is equal to

18. Let f(x) = x – x2 and g(x) = ax. If the area bounded by f(x) and g(x) is equal to area bounded by the curvesx = 3y – y2 and x + y = 3, then find the value of |a|.

19. Let A =

2 0 70 1 01 –2 1

and B =

–x 14x 7x0 1 0x –4x –2x

are two matrices such that AB = (AB)–1 and AB I (where is an identity matrix).

Then Tr((AB) + (AB)2 + (AB)3 + (AB)4 + (AB)5 + (AB)6)is equal to(where Tr(A) denotes the trace of matrix A).




20. At a point on the screen in YDSE experiment 3rd maxima is observed at t = 0. Now screen is slowly movedwith constant speed away from the slits in such a way that the centre of slits and centre of screen lie onsame line always and at t = 1 sec the intensity at that point is observed (3/4)th of maximum intensity inbetween 2nd and 3rd maxima. The speed of screen may be (D = separation between the screen and slits d =separation between the slits, d << D, = 5000 Å)

(A) 7D13 (B)

13D5 (C)

D17

(D) None of these

21. Five rods of the same dimensions are arranged as shown. They have thermal conductivities k1, k2, k3, k4 andk5. When points A and B are maintained at different temperatures, no heat flows through the central rod. Itfollows that

A B

k1 k2

k3 k4

k5

(A) k1 = k4 and k2 = k3 (B) k1/k4 = k2/k3

(C) k1k4 = k2k3 (D) k1k2 = k3k4

22. A point source of heat of power P is placed at the centre of a thin spherical shell of mean radius R. Thematerial of the shell has thermal conductivity k. If the temperature difference between the outer and innersurfaces of the shell is not to exceed T, the thickness of the shell should not be more than

(A) 24 kR T

P

(B) 24 kR

TP

(C) 24 R T

kP

(D) 24 R P

kT



PHYSICS


23. Consider a uniformly charged hemispherical shell shown below. Indicate the directions (not magnitude) ofthe electric field at the central point P1 and an off-centre point P2 on the drumhead of the shell.

(A) ;

(B) ;

(C) ;

(D) ;

24. The electric field intensity at the centre of a uniformly charged hemispherical shell is E0. Now two portions

of the hemisphere are cut from either side and remaining portion is shown in figure. If = = 3

, then

electric field intensity at centre due to remaining portion is :

(A) 3

E0

(B) 6

E0

(C) 2

E0

(D) Information insufficient

25. The resistance of each straight section is r. Find the equivalent resistance between A and B.

(A) 3 r (B) 3.5 r (C) 4 r (D) 4.5 r


PHYSICS




Paragraph for Question Nos. 26 to 28A man of mass 50 kg is running on a plank of mass 150 kg with speed of 8 m/s relative to plank as shown inthe figure (both were initially at rest and the velocity of man with resect to ground anyhow remains constant).Plank is placed on smooth horizontal surface. The man, while running whistles with frequency f0. A detector(D) placed on plank detects frequency. The man jumps off with same velocity from point D and slides on thesmooth horizontal surface [Assume coefficient of friction between man and horizontal surface is zero]. Thespeed of sound in still medium is 330 m/s. Answer following questions on the basis of above situations.

= 0 D

26. The frequency of sound detected by detector D, before man jumps of the plank is

(A) 0332 f324 (B) 0

330 f322 (C) 0

328 f336 (D) 0

330 f338

27. The frequency of sound detected by detector D, after man jumps of the plank is

(A) 0332 f324 (B) 0

330 f322 (C) 0

328 f336 (D) 0

330 f338

28. Choose the correct plot between the frequency detected by D Vs position of the man relative to detector

(A)

Frequency detected

Position of man relative to detector

f0 (B)

Frequency detected


f0

(C)

Frequency detected


f0(D)

Frequency detected


f0



Figure shows one experimental scheme for measuring the distribution of molecular speed. A substance isvaporized in source, molecules of the vapour escape through an aperture in the source . Slit blocks allmolecules except those in a norrow beam which is aimed at a pair of relatively rotating discs. A moleculepassing from the first disk is blocked by the second disk unless it arrives just as the slit in the second diskis lined up with the beam. This range of speed can be varied by changing disk rotation speed. We canmeasure how many molecules lie within each of various speed ranges, by the help of plotting a graph

between f(v) called distribution function and speed v. [f(v) = dv

dNv where dNv is the number of molecules with

speed from v to v + dv]

sourcex

disks

D detector

vacuum

Choose the correct answer29. Let the spacing between the two disks is x, and angular spacing between the slits on the disks is . Find the

velocity of a molecule able to pass through the 2nd disc rotating with an angular velocity , when first disc isstationary (R is radius of the disc).

(A) xv

(B) vR

(C) Rv

(D) Rv

30. If function f(v) described the actual distribution of molecular speed is f(v) = 22 bvav e , then the most probablespeed will be (Here, a and b are temperature dependent quantities)

(A) ab (B)

1a (C)

1b (D) None of these

31. The area shown under the distribution curve will give(A) Kinetic energy (B) Potential energy(C) Internal energy (D) Number of particles.






P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

32. A bird in air is diving vertically over a tank with speed 5 cms–1. Base of tank is silvered. A fish in the tank isrising upward along the same line with speed 2 cms–1. Water level is falling at a rate of 2 cms–1.(Take water = 4/3)

Column-I Column-II (in cms–1)(A) Speed of the fish as seen by the bird directly (P) 8(B) Speed of the image of fish formed after reflection in (Q) 6

the mirror as seen by the bird(C) Speed of the bird as seen by the fish directly (R) 3

(D) Speed of image of bird as seen by the fish looking (S) 4downward in the mirror.

(T) None of these



33. Before connecting the circuit shown in figure, all capacitors were uncharged. The circuit is in steady state.Now switch is closed. During the time the steady state is reached again, match the following

C1

C2

2 F

2 F

10v

10v 2 F

C3C4 2 F

10v

Column-I Column-II(A) Charge on C1 (P) Increases(B) Charge on C2 (Q) Decreases(C) Charge on C3 (R) Remain same(D) Charge on C4 (S) Becomes zero

(T) Always remain zero

PHYSICS



PHYSICS




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

34. A cart is pulled with a constant force F with a constant velocity v = 3 ms–1 on a smooth horizontal ground. Ahooper loads the cart with sands at a rate of 2 kg/s. Find the rate of mechanical energy loss. (in J/s)

F


PHYSICS


35. A capillary of radius r = 0.2 mm is dipped vertically in a liquid of density = 103 kg/m3. A small piston(x) isinserted inside the capillary which maintains constant pressure P1 = 0.5 × 105 N/m2 of air abovehemispherical meniscus. Atmospheric pressure P0 = 105 N/m2 and surface tension of liquid T = 10 N/m. Ifthe height of the liquid in capillary tube is found to be h = 5x meter, find the value of x.

36. Rod is massless and of length . Find angular frequency (in s–1) of small oscillation of the block of mass m,the hinge is frictionless. k1, k2, k3 are spring constants of the shown springs. Ignore gravity.

(k1 = k2 = 10 N/m, k3 = 154

N/m, m = 250 gm)

/2

k1

k2

k3



PHYSICS

37. A solid sphere of mass M of radius R is moving with speed 1GM 100 10 msR

in free space. Due to

applicaiton of external impulsive force, it breaks into eight spheres of equal radius in such a way that the totalmechanical energy before breaking and after breaking of a sphere remains same. The speed of each sphere(in m/s) when separation between them is very large is found to be 100x. Find the value of x(assume at that instant speed of each sphere is same).

38. Cylindrical bucket (B) with water in it has mass 10 kg balances a mass of 12 kg (A) on horizontal surface asshown in the figure. A piece of cork of mass m = 2 kg and specific gravity 0.5 is tied to the bottom of thebucket through a light string. A is moved horizontally with constant velocity 4 m/s as shown.Find the ratio of tension T1 and T2 at the instant A reaches point C.

A A1m60°

m

B

T1

T2

C




39. The equilibrium SO2Cl2(g) SO2(g) + Cl2(g) is attained at 25ºC in a closed rigid vessel. Helium gas isadded into the vessel. Which of following statement is correct ?(A) Concentration of Cl2 increased.(B) Concentration of SO2Cl2 increased.(C) Concentration of SO2Cl2, SO2 and Cl2 remains constant.(D) Concentration of SO2Cl2, SO2 and Cl2 decreases.

40. Select CORRECT representation of electrorefining of copper

(A) PureCu

ImpureCu Zn+2

CuSO + H SO44 2

Ag,Au

(B) PureCu

ImpureCu Zn

CuSO + H SO44 2

Ag,Au

(C) PureCu

ImpureCu Zn+2

CuSO + H SO44 2

Ag,Au

(D) PureCu

ImpureCu Zn

CuSO + H SO44 2

Ag,Au

41. HO(CH ) –C– OH2 3 (CH )2 3

OH+

Acetal

What is the relationship between products formed?(A) Enantiomers (B) Diastereomers (C) Positional Isomers (D) Functional isomers



CHEMISTRY


42. What is the pressure of 2 moles of a real gas ‘X’ at 27ºC, present in 5 L vessel?(a = 4.17 atm.L2.mol–2 , b = 0.037 L/mol)(A) 9.33 atm (B) 10.53 atm (C) 12.5 atm (D) 15.3 atm

43. Which of them is pair of most insoluble white compound and most insoluble coloured compound amongBaSO4, SrSO4, BaCrO4, SrCrO4(A) BaSO4 , BaCrO4 (B) BaSO4 , SrCrO4 (C) SrSO4 , BaCrO4 (D) SrSO4 , SrCrO4

44.

O

NO2

O

NH2

Above conversion can be achieved by(A) LiAlH4 (B) NaBH4

(C)

OH

OH, H+, LiAlH4, H3O

+ (D)

OH

OH, H+, H2/Ni, HO–



Comprehension TypeThis section contains 2 groups of questions. Each group has 3 multiple choice questions based on aparagraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE iscorrect.

Paragraph for Question Nos. 45 to 47Complexes X (Red) and Y (Yellow) have same formula Co.5NH3.NO2.Cl2 .1 mole of each X and Y both gives 2 moles of AgCl when react with excess of AgNO3.

45. Select CORRECT statement for X and Y(A) Both X and Y contain NO2

– as a ligand.(B) Both X and Y contain ONO– as a ligand.(C) X contain NO2

– while Y contain ONO– as a ligand.(D) X contain ONO– while Y contain NO2

– as a ligand.

46. X and Y both can show(A) Linkage isomerism (B) Ionization isomerism(C) Both linkage as well as ionization isomerism (D) Geometrical isomerism

47. Select CORRECT statement for X and Y(A) X and Y both are diamagnetic (B) X and Y both are paramagnetic(C) X is paramagnetic while Y is diamagnetic (D) X is diamagnetic while Y is paramagnetic




Electrode potential depends on ion concentrations and pressure of gas, it is possible to construct a cell fromtwo half cells composed of the same material but differing in ion concentrations.

Such a cell is called a concentration cell. Use : 2.303RT

F = 0.06 volt

48. The EMF of the following cell at 25°C is :Pt | H2 (g, 1bar) | HCl (aq) || HCl (aq) | H2 (g, 1 bar) | Pt

pH = 3.95 pH = 1.45(A) 0.075 V (B) 0.324 V (C) –0.15 V (D) 0.15 V

49. Carefully observe the given figure and using data provided find the EMF (in volt) of shown Galvenic cell :

Solution A is 0.1 M each in CH3COOH and CH3COONa and solution B is 0.1 M NH4Cl.[Given : Ka (CH3COOH) = 10–5 , Kb (NH4OH) = 10–5 ](A) 0.06 V (B) 0.12 V (C) 0.24 V (D) 0 V

50. Two beakers A and B contains AgNO3 solutions of concentrations 0.05 M and 0.01 M respectively as shownin figures. Pure silver electrodes are now lowered in each beaker. Now NH3 is added in each beaker till conc.of NH3 in beaker A and B become 0.1 M and 0.2 M respectively. If two beakers are now connected in Galvaniccell arrangement, find the EMF (in Volts) of the resulting cell at 298 K.

[Given : log102 = 0.3, f 3 2K [Ag(NH ) ] = 108]

Ag Ag

AgNO3 AgNO30.05 M 0.01 M

Beaker (A) Beaker (B)

(A) 9.6 × 10–2 (B) 7.8 × 10–2 (C) 5.8 × 10–3 (D) 9.6 × 10–3



CHEMISTRY





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

51. Column I Column II

(A) [Sc(H2O)6]3+ (P) Paramagnetic complex

(B) [Fe(H2O)6]3+ (Q) Diamagnetic complex

(C) [Co(H2O)6]3+ (R) Coloured complex

(D) [Cr(H2O)6]3+ (S) Colourless complex

(T) Inner orbital complex


CHEMISTRY



(A) ClPh H O2 (P) SN1

(B)Cl

Ph – S Na

(Q) SN2

(C)NO2

F KOH

(R) Carbocation is intermediate

(D) Br2

CCl4(S) Carbanion is intermediate

(T) Meso-product


CHEMISTRY




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

53. x = Number of structural isomer of C4H10O reacts with PhMgBr to gave as a product.

54. On the electrolysis of Na2MoOn, 0.112 lit of O2 at anode (1 atm, 0ºC) is obtained along with 0.32 gm of Mo atcathode, the value of n is



CHEMISTRY55. x = number of compound undergo nucleophilic substitution reaction

CH3–Cl, Cl,

Cl

NO2

,O

O–Et, OH, CH –CH=CH ,3 2

O

Cl, CH –C N3

56. Identify which product is/are formed as aromatic

(a) (b) NH3

O

O

(c) O

H

(d) (e)

Cl

Ag (f)

Cl

AlCl3

(g) CH MgBr3 (h)

COOH

COOH

O

57. A 75 g of 4%

ww

aqueous NaOH solution is vaporised for some time. The water vapours collected has a

mass of 32 g. To this remaning solution x g of KOH is added, so that molality of OH– ion the resulting solutionbecomes 5. Calculate the value of x ? (Consider all solutes are non-volatile)



CODE - A




11. Section II contains 2 groups of questions. Each groups has 3 questions based on aparagraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out ofwhich only one of correct.



C. Marking Scheme :

14. For each question in Section I, you will be awarded 5 marks if you darken thebubble corresponding to the correct answer and zero mark if no bubble is darkened.In case of bubbling of incorrect answer, minus two (–2) mark will be awarded.

15. For each question in Section II, you will be awarded 3 marks if you darken thebubble corresponding to the correct answer and zero mark if no bubble is darkened.In case of bubbling of incorrect answer, minus one (–1) mark will be awarded.



DATE : 16-08-15




















CODE - A


DATE : 13-09-15




1. The value of

x/11

0

x0x

dy))y–1(aby(lim

(where a b)

(A) a–b

1

a

b

ab

e1

(B)

a–b1

a

b

abe

(C)

a–b1

a

b

ab

(D)

a–b

a

b

abe

2. If f(1) = 3, f '(1) = 2 and f "(1) = 4 and let f–1 (x) = g(x) then g"(3) is equal to

(A) 41– (B) –1 (C) –2 (D)

21–

3. If A(n) represents the area bounded by the curve y = n ln x, where n N and n 2, the x-axis and the linesx = 1 and x = e. Then the value of A(n) + n A(n – 1) is equal to

(A) en2 (B) e

n2

(C) n2 (D) n

4. If f(x) = sin2x – 3 cos2x + 2ax – 4 is increasing x 0 then complete range of 'a' is(A) [–2, ) (B) [2, ) (C) (–, –2] (D) (–, 2]




MATHEMATICS5. The area (in sq. units) of the region consisting of points (x, y) which satisfy |x| 1 + |y| and |y| 1 is

(A) 4 (B) 6 (C) 8 (D) 12

6. The value of

......

542C–

432C

322C–1

43

1132

1121

11

upto 12 terms is equal to

(A) 111

(B) 121

(C) 131

(D) 141

7. The probability that a four digit natural number will contain exactly two distinct digits is

(A) 9000567

(B) 9000568

(C) 9000566

(D) 9000687

8. If c,b,a are non coplanar vectors such that acb , cba,bac , then which of the following is

not true

(A) |b||a| (B) 2|c||b||a| (C) [a b c] 1

(D) 1|c||b||a|



MATHEMATICS

9. In a triangle ABC if B – C = 45º and

–2 cosC cosBcosC –1 cos AcosB cos A –1

+ cos2A = 0, then a : b : c is equal to

(notations have their usual meaning)

(A) 1: 2 : 3 (B) 1 : 1 : 1 (C) 1: 3 : 2 (D) 1: 2 :1

10. Two circles pass through A (1, 2) and E(2, 1) touch the line 4x + 8y – 7 = 0 at B and D. The coordinates of Csuch that ABCD is a parallelogram is :

(A) 15 9,–2 2

(B) (0, 3) (C) 1 5,2 2

(D) 3 3,2 4

11. The lengths of two opposite edges of a tetrahedran are 12 and 15 units, their shortest distance is 10 units. Ifthe volume of the tetrahedran is 200 cubic units, then the angle between the two edge is :

(A) 3

(B) sin–113 (C) sin–1

23 (D) sin–1

35

12. Let diag.(a, b, c) represents a 3 × 3 diagonal matrix with diagonal elements a, b, c (in order). Now considermatrices A = diag(3, 2, 5), B = diag(11, 19, 13) and C = diag (61, 53, 31). The number of factors of trace ofmatrix ABC is :(A) 8 (B) 16 (C) 32 (D) 64



MATHEMATICS13. There are 'n' different gift coupons, each of which can occupy N (N > n) different envelopes with the same

probability 1 .N

P1 : The probability that there will be one gift coupon in each of 'n' definite envelopes out of N given envelopes.P2 : The probability that there will be one gift coupon in each of 'n' arbitrary envelopes out of N given envelopesconsider the following statements.

(i) P1 = P2 (ii) P1 = nn!N

(iii) P2 = nN!

N (N – n)! (iv) P2 = nn!

N (N – n)!

(v) P1 = nN!N

Which of the following is true.(A) Only (ii) (B) (ii) and (iii) (C) (ii) and (iv) (D) (iii) and (v)

14. There are 10 seats in the first row of a theatre of which 4 are to be occupied. The number of ways of arranging4 persons so that no two persons sit side by side is :(A) 7C4 (B) 4 7P3 (C) 420 (D) 960

15. There is a group of 6 persons. They play a game in which each has to select a number from 1, 2, 3, 4. Thegroup wins if atleast 5 of them have same selection of numbers, then the probability that the group wins is :

(A) 5194

(B) 6734

(C) 5184

(D) 6234

16. The value of

2

2x dx

51|x|

(A) 4 (B) 1 (C) 3 (D) 2



MATHEMATICS17. The number 915 – 715 is divisible by

(A) 8 (B) 7 (C) 2 (D) None of these

18. If (x) = xsinxtan

)x1(ne2x

then 0xlim

x)x(

equals

(A) –1 (B) 1 (C) 0 (D) 2

19. Let a curve y = f(x) satisfies y x2 + x(y)2 = 2xy; f(0) = 0 and f (1) = 1 ; then f(x) is :(A) 2(x – tan–1x) (B) 2(x – n(1 + x)2)(C) 2(n(1 + x2) – x) (D) 2(tan–1x – n(1 + x))

20. Two numbers x and y are choosen at random (without replacement) from the numbers 1, 2, 3, ........, 2004.The probability x3 + y3 is divisible by 3 is :

(A) 31

(B) 32

(C) 61

(D) 41



MATHEMATICS

21. The value of nlim

1n

1r2 )r–n(n

rn equals

(A) 2

(B) 2

1(C)

22

(D) 2

2–

22. Exhaustive set of the real values of m such that both roots of the equation x2 – 2mx + m2 – 1 = 0 are greaterthan –2 and less than 4, is(A) (–2, 4) (B) (–1, 2) (C) (–1, 3) (D) None of these

23. Let k2i3a

and kj2b

. If c

is a unit vector, then maximum value of ]cba[

is :

(A) 61 (B) 59 (C) 36.3 (D) 55

24. The number of values of ‘’ for which the system of equations( + 2)x + 4y = 2x + ( + 1)y = – 3

has infinitely many solution(A) 0 (B) 1 (C) 2 (D) Infinite


MATHEMATICS


25. If A =

11221112x

; x – 311

and |adj (adjA)| = (14)4 then the value of x is :

(A) 2 (B) – 2 (C) 0 (D) 1

26. The number of values of ‘r’ satisfying 69C3r–1 – 2r69 C = 1–2r

69C – r369C is/are

(A) 1 (B) 2 (C) 3 (D) 4

27. Let c,b,a

are three non-zero vectors and b

is neither perpendicular to a

nor to c

and

)ba(

× c

= a

× )cb(

. Then the angle between a and c

is :

(A) 6

(B) 3

(C) 2

(D) 0



MATHEMATICS28. The area enclosed between the lines y = 0 ; x = 0 , x = 2 and the curve f(x) = max. (cos–1(cosx), |x – |) is:

(A) 2

2(B)

23 2

(C) 22 (D) None of these

29. Let and are unit vectors and is a vector such that )( + = and

. Then the value of

][ .

(A) 0 (B) 1 (C) 2 (D) 3

30. Shortest distance between the lines bar

and r c d

equals

(A) 0 (B) [abc] – [cbd]

| b d |

(C)

[abd] – [cbd]| b d |

(D)

a.c a.b a.d| b d |




31. In order to measure the speed v of blood flowing through an artery, a uniform magnetic field B is applied in adirection perpendicular to the flow and a voltmeter measures the voltages V across the diameter D of theartery at right angles to B. If positive and negative ions in the blood are longitudinally at rest with respect tothe flow, the speed of flow is closest to

(A)B

VDv (B)V

BDv (C)BDVv (D)

VDBv

32. In the diagram shown, a non-uniform magnetic field B = B0x has been applied in the direction shown Aparticle of mass m and charge –q is projected with a velocity u from origin toward +ve x-axis. The displacementof the charged particle along x-direction when its velocity becomes parallel to y-direction, is

(A) 0qB

mu(B)

0qBmu2 y

x(C) 0qB2

mu(D)

0qBmu4

33. Spaceman Fred's spaceship (which has negligible mass) is in anelliptical orbit about Planet Bob. The minimum distance betweenthe spaceship and the planet is R; the maximum distance betweenthe spaceship and the planet is 2R. At the point of maximumdistance, Spaceman Fred is traveling at speed 0. He then fireshis thrusters so that he enters a circular orbit of radius 2R.What is his new speed?

(A) 02/3 (B) 05 R 2R

(C) 05/3 (D) 02



PHYSICS


34. Consider the situation shown in figure. The straight wire is fixed but the loop can move under magnetic force.The loop will(A) Remain stationary

i1

i2

(B) Move toward the wire(C) Move away from the wire(D) Rotate about the wire

35. A gas is enclosed in a vessel at a constant temperature at a pressure of 2.0 atmosphere and volume 4 litres.Due to a leak in the vessel. after some time the pressure is reduced to 1.5 atmosphere. As a result the(A) 25% of the gas has escaped out. (B) 50% of the gas has escaped out.(C) 75% of the gas has escaped out. (D) 100% of the gas has escaped out.

36. A uniformly charged ring of radius R is rotated about its axis with constant linear speed v of each of itsparticles. The ratio of electric field to magnetic field at a point P on the axis of the ring distant x = R fromcentre of ring is (c is speed of light).

(A) v

c2(B)

cv2

x=RPO

v

(C) vc

(D) cv


PHYSICS


37. The Pitot tube shown in the figure is used to measure fluid (gas) flow velocity in a pipe of cross sectional areaS. It was invented by a French engineer Henri pitot in the early 18th century. The volume of the gas flowingacross the section of the pipe per unit time is (The difference in the liquid columns is h, 0 and are thedensities of liquid and the gas respectively)

(A) Q = 2S gh 0 (B) Q = S

gh2 0

Differencein pressure

Area S

h

Liquid(C) Q = S

0hg(D) Q = S

0

gh2

38. An infinite line charge with positive charge is kept on x-axis. Treat x-y plane as horizontal. An electron is keptbelow x axis hanging in space in equilibrum. It’s equilibrium is :(A) Stable if allowed to move only parallel to x axis.(B) Stable if allowed to move only parallel to y axis.

x

y

z

(C) Neutral if allowed to move only parallel to x axis.(D) Stable if allowed to move only parallel to z axis.

39. A point source of power 50 watts is producing sound waves. The velocity of sound is 330 m/s, density of air

is 1.0 kgm–3. Then (using = 22/7) at r = 330 m from the point source.

(A) Pressure amplitude is 10 Nm–2 (B) Pressure amplitude is 5 Nm–2

(C) Pressure amplitude is 6 Nm–2 (D) Pressure amplitude is 12 Nm–2


PHYSICS


40. Heat produced in the circuit shown in the figure, when switch is closed is :

10V

4 4

5F 5F

5F

4

(A) 125 J (B) 250 J (C) 375 J (D) 500 J

41. Two equal masses are attached to the two ends of spring of spring constant k. The masses are pulled outsymmetrically to stretch the spring by a length x over its natural length. The work done by the spring on eachmass is :

(A) 21 kx2

(B) 21– kx2

(C) 21 kx4

(D) 21– kx4

42. Two vessels A and B of cross-sections as shown contain a liquid up to the same height. As the temperaturerises, the liquid pressure at the bottom (neglecting expansion of the vessels) will(A) Increase in A, decrease in B(B) Increase in B, decrease in A(C) Increase in both A and B A B(D) Decrease in both A and B


PHYSICS


43. Two glass slabs of same thickness are joined to form an L as shown. A ray is incident on the combination asshown (in the plane of paper). The final emergent ray will

45º

t

At

(A) Come out at point A in the same direction as that of the original ray.(B) Come out at point A but not in the same direction as that of the original ray.(C) Does not come out at point A but is in the same direction as that ofthe original ray.(D) Does not come out at point A and is not in the same direction as that of the original ray.

44. Mary sits on the perimeter of a merry-go-round of radius 2m undergoing uniform circular motion. Matt standson the ground 6m from the centre of the merry-go-round. Matt observes Mary coming towards him at a speedof 1 m/s. What is Matt’s speed from the point of view of Mary ?

(A) 2 m/s (B) 3 m/s (C) 10 m / s (D) 1 m/s

45. In the circuit shown, current (in A) through the 50 V and 30 V batteries are, respectively :

20 105

5

50V 30V

(A) 3 and 2.5 (B) 3.5 and 2 (C) 4.5 and 1 (D) 2.5 and 3


PHYSICS


46. The displacement of a string carrying a traveling sinusoidal wave is given by y(x, t) = ymsin(kx – t –). Attime t = 0 the point at x = 0 has a transverse velocity of 0 and a positive displacement. The phase constant is :(A) /4 (B) /2 (C) 3/4 (D) 3/2

47. A string is firmly attached at both ends. When a frequency of 60 Hz is applied, the string vibrates in thestanding wave pattern as shown. Assume the tension in the string and its mass per unit length do notchange. Which of the following frequencies could NOT also produce a standing wave pattern in the string?

(A) 30 Hz (B) 40 Hz (C) 80 Hz (D) 100 Hz

48. A cart is pulled along a horizontal track by a rope that passes over a fixed pulley, as shown in the figure.Assume the tension in the rope and the frictional foces on the cart remain constant. As the cart moves to theright, its acceleration.

Constant force fixedpulley

(A) Decreases (B) Increases (C) Remains constant (D) is zero


PHYSICS


49. A cubical block (a × a × a), with a coin of mass 'm' over it is floating over a liquid of density . In this case x1depth of the block is immersed. Now the coin is removed & it is found that x2 depth is immersed in liquid.Value of (x1 – x2) is

x

m

(A) 2ma (B)

4am

(C) 2m

2 a (D) Data insufficient

50. Resistance of ammeter is r and emf and internal resistance are shown in the circuit then reading of ammeteris :-

, r

2 2, r

3 3, r

4, 4r A

(A) 23r

(B) 4r

(C) r

(D) None of these

51. Two particles approach each other with different velocities. After collision, one of them is found to have

momentum p

in their centre of mass frame. In the same reference frame, the other particle must have

momentum

(A) zero (B) p2

(C) p

(D) 2p


PHYSICS


52. Each of the three balls shown has been given either a positive or a negative charge or it has been given nocharge. We find that balls A and B attract each other and balls B and C repel each other.(A) One of the balls has no charge

A B B C

(B) Balls A and C carry charges of opposite sign(C) Balls A and C carry charges of the same sign(D) We need to do more experiments to draw any of the above conclusion.

53. The distance of centre of mass of an uniform circular sector shaped plate from centre O is :

(A) 2R/3 (B) 0

0

2Rsin2

0

O

R

(C) 0

0

sin4R 23

(D) 4R/3

54. A bomb is projected upwards. At topmost point it explodes in three identical fragments. First fragmentcomes to ground in 10 second and other two in 20 second each. Then the height reached by the originalbomb is :(A) 800m (B) 1600m (C) 1250m (D) 1500m



PHYSICS55. A monochromatic light is used in Young’s double slit experiment, When one of the slit is covered by a

transparent sheet of thickness 1.8 ×10–5 m, made of a material of refractive index µ1, the number of fringeswhich shift is 18. When another sheet of thickness 3.6 × 10–5 m, made of a material of refractive index µ2 isused, the number of fringes which shift is 9. Then, the relation between µ1 and µ2 is given by(A) 4µ2 –µ1 = 3 (B) 4µ1 –µ2 = 3 (C) 3µ2 –µ1 = 4 (D) 2µ1 – µ2 = 3

56. Two identical wires of same length are bent into the shapes as shown in the figure. The ratio of magnitude ofmagnetic field at P1 to magnetic field at P2 is

(A) 28 2

(B) 224

P1 P2

l

2l

l

l l l

i i(C) 1 (D) 2

57. A neutral particle is initially at rest in a uniform magnetic field B. The particle then spontaneously decays intotwo fragments, one with a positive charge +q and mass 3m and the other with a negative charge –q and massm. Neglecting the interaction between the two charged particles and assuming that the speeds are muchless than speed of light, determine the time after the decay at which the two fragments first meet. Both thecharges have initial velocities in x-y plane and field is parallel to z-axis.

(A) qBm6

(B) qBm2

(C) qBm8

(D) qBm

23



PHYSICS58. A retro reflector is an optical device which reflects light coming from infinity back directly. Recently “Scotchlite”

sphere have been invented which behave as a retroreflector (figure). The index of refraction () for such sphereis :

(A) 23

(B) 2

\\\\\\\\\

\\\\\\

\\\

\\\

(C) 34n (D) No such value possible

59. A block of mass m kg is kept in touch with a spring of spring constant k N/m on a smooth inclined plane ofangle of inclination . We compress the block and release. What can be the maximum compression (in cm)so that the block does not lose contact with the spring at any time during the motion ?

(A) mgk

(B) kcosmg

(C) ksinmg

(D) ksinmg2

60. A body of mass 2 kg is suspended on a spring of spring constant 200 N/m, we shift the body from position

of equilibrium vertically downward to distance x0 and release. Determine distance traversed by the body

(in cm) during the time interval from t1 = T4

to t2 = 3T .8 Here x0 is the stretch of the spring in equilibrium

position and T is time period of its oscillations.

(A) 10 cm (B) cm25 (C) cm)1–2(5 (D) 5 cm




61. Select the INCORRECT order for given properties(A) LiH > NaH > KH > RbH (order of covalent character)(B) CdCO3 > CaCO3 > K2CO3 (order of thermal stability)(C) BeF2 > BaF2 > SrF2 > CaF2 > MgF2 (solubility in water)(D) BaCO3 < SrCO3 < CaCO3 (solubility in water)

62.

Product B is

(A)

OHC–O–C–CH3

O O

(B)

O–C–CH3

CO H2

O

(C)

O–C–CH3

CHO

O

(D)

C–O–CH3

CO H2

O

63. A compound X dimerises in water, if its observed molecular weight and theoretical molecular weight are161.84 and 94 respectively. The % degree of association of compound X will be(A) 84 (B) 60 (C) 80 (D) 45

64. The INCORRECT order of boiling point is(A) H2S < H2Se < H2Te < H2O (B) H2S < NH3 < HF < H2O(C) PH3 < ASH3 < SbH3 < NH3 (D) HCl < HBr < HI < HF




CHEMISTRY65. In which of the following diastereomeric mixture formed

I. II.

O

NH –OH2

H+

III.

O

2, 4 DNP IV.

NOH

H SO2 4

(A) I, II only (B) I, II and III only (C) II and III only (D) II, III and IV

66. EºOP of following reaction isAg(s) + 2NH3(aq) Ag (NH3)2

+ (aq) + e–

Given : Kf ))NH(Ag( 23 = 1016 ; o

Ag | AgE 0.80V

(A) 0.1456 V (B) +1.746 V (C) –0.1456 V (D) –1.746 V

67. Correct order of P-P bond length in following compounds is(A) P2F4 < P2 (CH3)4 < P2 (CF3)4 < P2H4 (B) P2F4 < P2(CF3)4 < P2(CH3)4 < P2H4(C) P2F4 < P2H4 < P2 (CH3)4 < P2(CF3)4 (D) P2F4 < P2(CH3)4 < P2H4 < P2(CF3)4



CHEMISTRY

68. CH3

Ph

Et

O

NH2

NaOBr CHCl3P1 P2KOHH2 P3Ni

product P3 is(A) 1° amine (B) 2° amine (C) 3° amine (D) 1° amide

69. Conversion of 'A' isomer of a compound to 'B' isomer of same compound follows reversible first order kineticswith equilibrium constant equal to 10. Starting with 0.1 M of 'A' isomer only, calculate concentration of 'A'isomer 60 sec after the start, if rate constant of forward reaction is 0.063 min–1.(A) 0.08 M (B) 0.095 M (C) 0.04 M (D) 0.0545 M

70. Tin is extracted from cassiterite ore by(A) Electrolytic reduction (B) Carbon-monoxide reduction(C) carbon reduction (D) aluminothermic process

71. (2R)-2-Phenyl butan-2-ol + O N2 C–Cl

OPyridine Product is

(A)

CH3

CH2–CH3

C

O

O NO2 (B)

CH –2 CH3

CH3

C

O

OO2N

(C)

CH –2 CH3

CH3

C

O

O NO2 (D) CH –2 CH3

CH3

O

O

CO2N


CHEMISTRY


72. Statement-1 At low pressure and high temperature, the value of compressibility factor Z is unity.becauseStatement-2 When pressure is extremely low attractive forces play significant role in daviation from ideal

behavior.(A) Statement-1 is true, Statement-2 is true and Statement-2 is correct explanation for Statement-1(B) Statement-1 is true, Statement-2 is true and Statement-2 is NOT the correct explanation for Statement-1(C) Statement-1 is true, Statement-2 is false(D) Statement-1 is false, Statement-2 is true

73. Which of the following has largest number of isomers ?(A) [Co(en)2Cl2]

+ (B) [Co(NH3)5Cl]2+ (C) [Ir(PR3)2H(CO)]2+ (D) [Ru(NH3)4Cl2]+

74. CH3

Br

NBS H O, CaCO2 3G H PCCCH Cl2 2

I

Incorrect statement regarding above reaction sequence.

(A) G is Br

Br

(B) H is

Br

OH

(C) I is

OH

O (D) I is

Br

O



CHEMISTRY75. The specific conductance of a 0.20 M solution of an electrolyte at 20ºC is 2.48 x 10–4 ohm–1cm–1.

The molar conductivity of the solution is -(A) 1.24 ohm–1 cm2 mol–1 (B) 4.96 ohm–1 cm2 mol–1

(C) 1.24 ohm–1 cm2 (D) 4.96 ohm–1 cm2

76. Which of the following will have three stereoisomeric formes ?(i) [Cr(NO3)3(NH3)3] (ii) K3[Co(C2O4)3] (iii) K3[CoCl2(C2O4)2] (iv) [CoBrCl(en)2](A) (iii) and (iv) (B) (i), (iii) and (iv) (C) (iv) only (D) all four

77.

C–NH2

O

CH3

C–NH2

O

C H2 5

andOH/Br2 Products are

(intramolecular migration)

15

(A)

NH2

CH3

and

NH2

Et

15

(B)

NH2

and

CH3

NH2

15

Et

(C)

NH2

CH3

NH2

Et

15

and(D)

NH2

and

CH3

NH2

15

Et



CHEMISTRY78. 16 g of a radioactive substance is reduced to 0.50 g after 1 hour. The average life of the radioactive substance is

(A) 10 min (B) 12 min (C) 15 min (D) 17.3 min

79. Which is INCORRECT statement ?(A) Poling process is used to remove Cu2O from Cu(B) Cupellation process is used to remove traces of lead from silver(C) Liquation process is used for purification of metals whose melting point are higher than those of impurities(D) Extraction of lead from galena involves roasting at moderate temperature followed by self reduction at

high temperature

80.O O

NH2

(i) Br /KOH2

(ii) H /+ Product is

(A) O

NH2(B)

ONH2

HO

(C)

O

NH (D)

O

O



CHEMISTRY81. The ratio of mole fraction of A at point P and point Q in following graph is :

QP

200

140100

pure B pure A

Pressure(torr)

composition(mole fraction of A)

(A) 0.40 (B) 0.57 (C) 0.702 (D) 1.429

82. K3[Fe(CN)6] + Mx+(aq) ppt of complex saltWhich of the following cation does not respond above reaction.(A) Cu2+(aq) (B) Fe3+(aq) (C) Zn2+(aq) (D) None of these

83. Find product(s) is :

(A) CO H2

(B)

CO H2OH

OH

(C) O,

CO H2

HO C2 (D) O , CO , CH CO H2 3 2–

84. Depression in freezing point of 0.01 m aqueous solution of HA is 0.01924 K. The pH of 0.01 M aqueoussolution of NaA is :[Given molarity = molality, Kf(H2O) = 1.85 K kg mol–1](A) 5.6 (B) 8.4 (C) 9.4 (D) 11.2



CHEMISTRY85. Softening of leads means

(A) conversion of lead to PbO (B) conversion of lead to Pb3O4(C) removal of impurities from lead (D) washing lead with HNO3 followed by alkali solution

86. Ph – C – CH – C – OH2

O O

A + B (gas)EtMgBr

Product

Product is

(A) Ph – C – CH3

O(B)

Ph – CH – CH3

OEt

(C) Racemic mixture of Ph – C – CH3

OH

Et

(D) Ph – C – CH3

OH

Et(optically pure)

87. In 103 litre sample of hard water CaSO4 and MgSO4 present. If elevation in boiling point is 0.000052 ºC.The degree of hardness of hard water is [Kb(H2O) = 0.52 K kg mol–1](A) 2.5 (B) 5.0 (C) 7.5 (D) 10.0



CHEMISTRY88. Which is not correctly matched

(1) Copper Glance : Cu2S (2) Pyrolusite : MnO2(3) Malachite : CuCO3.Cu(OH)2 (4) Cinnabar : PbS(A) 1 only (B) 2 only (C) 4 only (D) 1 and 4

89.

P and Q respectively are

(A)

O–C–CH3

O

,

O

OH

NH–C–CH3NH2

(B) ,

ONH–C–CH3NH2

C–O–CH3

OC–O–CH3

O

(C)

OH

,

ONH–C–CH3

C–O–CH3

O

ONH–C–CH3

(D)

OH

,

ONH–C–CH3

O–C–CH3

O

ONH–C–CH3

90. For the change H2O (s) at 273 K & 1 atm pressure H2O() at 273 K & 2 atm. The correct statement is:(A) G = 0 (B) G < 0 (C) G > 0 (D) Can not predict




C. Marking Scheme :



CODE - ADATE : 13-09-15




















CODE - A


DATE : 11-10-15




1. Let ABC be a triangle whose vertices are A(–5, 5) and B(7, –1). If vertex C lies on the circle whose directorcircle has equation x2 + y2 = 100; then the locus of orthocentre of ABC is(A) x2 + y2 + 4x – 8y – 30 = 0 (B) x2 + y2 – 4x + 8y – 30 = 0(C) x2 + y2 – 4x – 8y – 30 = 0 (D) x2 + y2 + 4x + 8y – 30 = 0

2. General solution of dxyx

y–xydy

yx1

xx1

22

3

2

2

2

is

(A) x2 + y2 + 2xy = c (B) x2 – y2 + x2y2 = cxy (C) y2 – x2 + x2y2 = c (D) None of these

3. If f(x) = f(4020 – x) x R and dx)x(fkdx)x(xf2011

2009

2011

2009 then the value of k equals

(A) 2010 (B) 2020 (C) 2030 (D) 2040



MATHEMATICS


4. If tangents drawn to circle |z| = 4 at points A(z1) and B(z2) intersect at P such that arg2z

z

1

2

then locus

of P is

(A) |z| = 2 (B) 24|z| (C) 22|z| (D) |z| = 8

5. For > 0, let the volume of the parallelopiped whose adjacent edges are k4j3i2a , k2jib

and ˆ ˆ ˆc i 2j k

is 15, then the value of equals to

(A) 25

(B) 27

(C) 29

(D) 2

13

6. Number of positive integers which have no two digits identical with sum of their digits being 45 is

(A) 10 (B) 9 (C) 99 (D) 8.17

7. A vertor equation of curve in three dimentional space denoted by k)3t(j)2t(i)2–tt(r 22

represents(A) a plane passing through origin (B) a plane passing through (0, 0, 1)

(C) a line parallel to the vector k–j5i (D) a line passing through (1, 1, 1)


MATHEMATICS





Let f(x, y) = x2 – y2 and g(x, y) = 2xy such that (f(x, y))2 – (g(x, y))2 = 21

and f(x, y) . g(x, y) = 43

.

8. Number of ordered pair(s) of (x, y)(A) 2 (B) 4 (C) 6 (D) 8

9. Product of all possible value(s) of x be

(A) 81

(B) 381

(C) 161

(D) None of these


MATHEMATICS


Paragraph for Question Nos. 10 to 12A tennis tourhament is arranged for 2n players. It is organised as a knockout tournament, so that only thewinner in any given round proceed to the next round. Opponents in each round except the final are drawn at

random, and in any match either player has a probability 21

of winning. Two players are choosen at random

before the start of the first round. Find the probability that they play each other

10. In the first round

(A) n2

2 6(B)

1–21

n (C) n3

2 5(D) n

22 2

11. In the final round

(A) 1–2

1n (B) )1–2(n

2n (C) )1–2(2

2nn (D) 1–n2

1

12. In the tournament

(A) 1–2

1n (B) 1–n2

1(C) )1–2(n

2n (D)

21


MATHEMATICS




13. Let }x{1

x)x(f

(where {·} denotes fractional part function) then

(A) 2013)2013(flim x

0x

(B) 1)2013(flim x

0x –

(C) e)2013(flim x

0x

(D) )2013(flim x

0x – does not exist

14. If the image of the line x = y + 1 in line 2x = 3y – 1 be ax – by + c = 0 then(a, b, c are relatively prime positive integers)(A) a, b, c are in A.P. (B) a, b, c are prime numbers(C) a, b, c are sides of a triangle (D) a < b < c


MATHEMATICS


15.

)1e(xtan

xe–x2lim 2

2

x

x

0x equals

([·] denotes greatest integer function)

(A) dx|xsin|41

2

0

(B) n–1nn

limn

(C) )xsecn(xcotlim2

x

(D) )xx1(n)xx–1(nxsec–xcoslim 220x

16. Let P1 denotes the equation of the plane to which the vector )ji( is normal and which contains the line

)kji()kji(r:L . P2 denotes the equation of the plane containing the line L and a point with

position vector j . Which of the following holds good?

(A) Equation of P1 is x + y = 2

(B) Equation of P2 is ˆ ˆ ˆr · ( i 2 j k) 2

(C) Acute angle between P1 and P2 is )3(cot 1–

(D) Angle between the plane P2 and line L is )3(tan 1–


MATHEMATICS




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

17. Let P(z) = z3 + az2 + bz + c where a, b, c R there exists a complex number w such that the three roots ofP(z) = 0 are w + 3i, w + 9i and 2w – 4 where i2 = –1. Find the unit digit of the sum |a + b + c|.

18. A line with direction ratios 2, 1, 2 meets the line x = y + 2 = z and x + 2 = 2y = 2z at P and Q respectively.Find the length of PQ.


MATHEMATICS


19. Let /4

nn

0

tan x dx ;

n = 0, 1, 2, ...... and

n

0nnS (In In + 1 + In In + 3 + In + 1 In + 2 + In + 2 In + 3).

Find the value of nnSlim

.

20. Find the unit digit of the sum k–6r–12

r

0kk

r CC


MATHEMATICS


21. Let x + y = 3e2. If the maximum value of xy can be expressed 2ee . Find .

22. Let the sum of all divisors of the form 2p . 3q (where p and q are positive integers) of the number N = 1988 – 1be . Find the unit digit of .

23. Let O be the interior point of ABC such that 0OC6OB3OA2 where 'O' is origin.

If nm

)AOB(ofArea)ABC(ofArea

, where m and n are relatively prime positive integers. Find the value of (m – n).




24. A point moves in a straight line under the retardation av2. If the initial velocity is u, the distance covered in ‘t’seconds is : (Assume “a” as a positive constant)

(A) a u t (B) 1 l n(a u t)a (C)

1 l n(1 a u t)a

(D) a l n (a u t)

25. A satellite is launched in the equatorial plane in such a way that it can transmit signals upto 60° latitudeon the earth. The angular velocity of the satellite is :

(A) 3GM8R

(B) 3GM2R

(C) 3GM4R

(D) 33 3GM

8R

26. In the figure shown water is filled in asymmetrical container. Four pistonsof equal area A are used at the four openings to keep the water inequilibrium. Now an additional force F is applied at each piston. Theincrease in the pressure at the centre of the container duie to thisaddition is

(A)FA

(B) 2FA

F

F

F

F(C) 4FA

(D) 0



PHYSICS


27. Earthquakes generate sound waves inside Earth. Unlike a gas, Earth can experience both transverse (S)and longitudinal (P) sound waves. Typically, the speed of S waves is about 4 km/s. A seismograph recordsP and S waves from an earthquake. The first P waves arrive 3.0 min before the first S wave (figure).Assuming the waves travel in a straight line, how far away does the earthquake occur? (Yearth=12.8 ×1010pa, earth = 2000kg/m3)

Time (min)1 2 3 4 5 6

P waves S waves

Dis

plac

emen

t of

seis

mog

raph

reco

rdin

g pe

n

(A) 1900 km (B) 1440 km (C) 1800 km (D) 1200 km

28. Two point dipoles p k & p k2 are located at (0, 0, 0) & (1m, 0, 2m) respectively. The resultant electric field due

to two dipoles at the point (1 m, 0, 0) is :

(A) 0

9p k32 (B) 0

–7p k32 (C) 0

7p k32 (D) none of these


PHYSICS


29. Circuit for the measurement of resistance by potentiometer is shown. The galvanometer is first connectedat point A and zero deflection is observed at length P J = 10 cm. In second case it is connected at pointC and zero deflection is observed at a length 30cm from P. Then the unknown resistance X is

GQ

CxAR

P J

(A) 2R (B) R2

(C) R3

(D) 3R

30. In a photoelectric experiment, the collector plate is at +2.0V with respect to the emitter plate made of copper

= 4.5eV). The emitter is illuminated by a source of monochromatic light of wavelength 200nm.(A) The minimum kinetic energy of the photoelectrons reaching the collector is 0.(B) The maximum kinetic energy of the photoelectrons reaching the collector is 3.7eV.(C) If the polarity of the battery is reversed then answer to part A will be 0.(D) If the polarity of the battery is reversed then answer to part B will be 1.7eV.


PHYSICS




Paragraph for Question Nos. 31 to 32An infinitely long wire lying along z-axis carries a current I, flowing towards positive z-diretion. There is noother current, consider a circle in x-y plane with centre at (2 meter, 0, 0) and radius 1 meter. Divide the circle

in small segments and let d denote the length of a small segment in anticlockwise direction, as shown.

dl1m

x (2,0,0)I

y

31 The path integral B.d of the total magnetic field B along the perimeter of the given circle is,

(A) 0I8 (B)

0I2 (C) 0I (D) 0

32 Consider two points A(3, 0, 0) and B(2, 1, 0) on the given circle. The path integral

B

A

B.d of the total

magnetic field B along the perimeter of the given circle from A to B is,

(A) –10I 1tan12 2 (B)

–10I 1tan2 2 (C)

–10I 1tan2 2 (D) 0



Huygen was the first scientist who proposed the idea of wave theory of light. He said that the light propagatesin form of wavefronts. A wavefront is an imaginary surface at every point of which waves are in the samephase. For example the wavefronts for a point source of light is collection of concentric spheres which havecentre at the origin, w1 is a wavefront, w2 is another wavefront.

W1

W2

Ray of lightS

The radius of the wavefront at time ‘t’ is ‘ct’ in this case where ‘c’ is th speed of light. The direction ofpropagation of light is perpendicular to the surface of the wavefront. The wavefronts are plane wavefrontsin case of a parallel beam of light.

Ray W , W , W wave front1 2 3

Huygen also said that every point of the wavefront acts as the source of secondary wavelets. The tangentdrawn to all secondary wavelets at a time is the new wavefront at that time. The wavelets are to beconsidered only in the forward direction(i.e. the direction of propagation of light) and not in the reverse

direction. If a wavefront w1 at time t is given, then to draw the wavefront at time t + t take some points

on the wavefront w1 and draw spheres of radius’c t’. They are called secondary waveles. Draw s surface

w2 which is tangential to all these wavelets. w2 is the wavefront at time ‘t + t’.

Secondary waveletof radius c t

w2

t + t

S

w1 t

Huygen proved the laws of reflection and laws of refraction using concept of wavefronts.



PHYSICS33. Spherical wave fronts shown in figure, strike a plane mirror. Reflected fronts will be as shown in

(A) (B) (C) (D)

34. Wavefronts incident on an interface between the media are as shown in the figure. The refracted wavefrontswill be as shown in

45°

1 = 1 = 22

(A) 30°

(B) 30°

(C) 60°

(D) 60°

35. The wavefront of a light beam is given by the equation x + 2y + 3z = c, (where c is arbitrary constant)then the angle made by the direction of light with the y-axis is :

(A) –1 1cos

14(B)

–1 2sin14

(C) –1 2cos

14(D)

–1 3sin14





36. A wire, under tension between two fixed points A and B, executes transverse vibrations so that the midpointO of AB is a node. Then :

A BO

(A) All points of wire between A and B are in the same phase.(B) All points between A and O are in the same phase(C) A point between A and O and a point between O and B may have a phase difference of /2(D) A point between A and O and a point between O and B may have a phase difference of

37. AB is part of a circuit as shown, that absorbs energy at a rate of 50W. E is an emf device that has nointernal resistance.

E

i = 1A

2A B

(A) Potential difference across AB is 48V.(B) Emf of the device is 48V.(C) Point B is connected to the positive terminal of E(D) Rate of conversion from electrical to chemical energy is 48 W in device E.


PHYSICS


38. A charged particle of charge q, mass m is moving with initial velocity ‘v’ as shown in figure in a uniform

magnetic field – ˆBK . Select the correct alternative/alternatives:

XX

XXX

XXX

XXX

XXX

X X XX XB

X

vq,m 30°

y

X

extend upto alarge distance

(A) Velocity of particle when it comes out from magnetic field is ˆv=v cos60º i v sin60º j

(B) Time for which the particle was in magnetic field is m3qB

(C) Distance travelled in magnetic field is mV3qB

(D) The particle will never come out of magnetic field

39. A block of mass 1 kg is stationary with respect to a conveyer belt that is accelerating with 1 m/s2 upwards atan angle of 30° as shown in figure. Which of the following is/are correct ?

30°

1kg

1 m/s2

(A) Force of friction on block is 6N.(B) Force of friction on block is 1.5 N.

(C) Contact force between the block & belt is 111 N.

(D) Contact force between the block & belt is 35 N.


PHYSICS




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

40. A charge q is divided into three equal parts and placed symmetrically on a circle of radius r. The same chargeis divided into four equal parts and placed symmetrically on the same circle. The electric field intensities atthe centre of the circle in two situations are zero.If a charge (part charge) is removed from one location in boththe situations and the ratio of magnitudes of the electric field intensities at the centre is(n+1)/n.Find n.


PHYSICS


41. If current in the branch CD of the circuit is 8+n amperes,find n.

DA

B

C

30V

3

2 22

42. An particle is moving along a circle of radius R with a constant angular velocity . Point A lies in thesame plane at a distance 2R from the centre. Point A records magnetic field produced by particle. Ifthe minimum time interval between two successive times at which A records zero magnetic field is 2/9 seconds, then find angular speed in radians/ sec.


PHYSICS


43. A block of mass m is placed on top of a block of mass 2m which in turn is placed on fixed horizontal surface.The coefficient of friction between all surfaces is = 1. A massless string is connected to each mass andwraps halfway around a massless and frictionless pulley, as shown. The pulley is pulled by horizontal force

magnitude F = 6 mg towards right as shown. If the magnitude of acceleration of pulley is 5 2X

m/s2, fill the

value of X. (Take g = 10 m/s2)

2m

m F = 6mg

44. Photons of energy 5eV are incident on cathode as shown in the figure. Electrons reaching the anode havemaximum kinetic energy 8eV.

h

5V

Find the work function of the metal.


PHYSICS


45. In the arrangement as shown in fig., pulleys are small and springs are identical with all spring constants

equal to K (= 32 N/m). If period of small vertical oscillations of block of mass m is eff

m2K

. Then find Keff.

K1

K2

K3

K4

m

46. An LCR series circuit with 100 resistance is connected to an AC source of 200 V and angular frequency300 radians/sec. When only the capacitance is removed.. The current lags behind the voltage by 60°. Whenonly the inductance is removed the current leads the voltage 60°. Calculate the current in the LCR circuit.




47. Which is not precipitate exchange reaction.(A) PbCl2 + 2NaOH Pb(OH)2 + 2NaCl(B) BaCO3 + H2SO4 BaSO4 + CO2 + H2O(C) Ag2CO3 + CH3COOH CH3COOAg + CO2 + H2O(D) ZnSO4 + Pb(NO3)2 PbSO4 + Zn(NO3)2

48. What is correct sequence of reagents to convert CH3–CH2–COOH into CH3–COOH ?I : Br2/KOH ; II : NaNO2/dil. HClIII. NH3/IV : KMnO4 /H

, V : Red P/Br2(A) V III IIV (B) V I IIIIV (C) III I IIIV (D) III II IIV

49. Cation of which metal hydroxide is soluble in excess NaOH solution(A) Ca2+ (B) Be2+ (C) Fe3+ (D) Mg2+

50. The product of electrolysis of dilute solution of NaCl using inert electrodes(A) O2 (g) at cathode, H2 (g) at anode (B) Cl2 (g) at anode, Na (s) at cathode(C) Cl2 (g) at anode, H2 (g) at cathode (D) O2 (g) at anode, H2 (g) at cathode



CHEMISTRY


51. Identify the final product (Y)

OH

CH3

(i) CHCl /KOH(aq)3

(x)

(ii) Zn–Hg(y)

Conc. HCl/

(p-cresol)

(A)

OH

CH3

CH3

(B)

OH

CH3

CH3

(C)

OH

CH3

CH –OH2

(D)

OH

CH3

COOH

52. All decomposition product(s) of which salt can react with NaOH solution(A) BeCO3 (B) MgCO3 (C) CaCO3 (D) BaCO3

53.

COOH

(Benzoic acid)

OH

(Phenol)

and can be distinguished by –

(A) NaOH (B) NaNH2 (C) Na metal (D) NaHCO3



Comprehension TypeThis section contains 2 paragraphs. Based upon the first paragraph, 2 multiple choice questions and basedupon the second paragraph 3 multiple choice questions have to be answered. Each of these questions hasfour choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Question Nos. 54 to 55The concept of co-ordination compounds arises from the complex formation tendency of transition elements.These compounds play a vital role in our lives, as chlorophyll of plants, vitamin B12 and haemoglobin ofanimal blood are the co-ordination compounds of Mg, Co and Fe respectively. The co-ordination compoundsplay important role in analytical chemistry , polymerisation reactions, metallurgy and refining of metals,photography, water purification etc. Co-ordination compounds also find many applications in electroplating,textile dyeing and medicinal chemistry.

54. What is the IUPAC name of [Co(en)2(NCS)2]NO3

(A) Bis(ethylene diamine) dithiocyanato-N cobalt((II)Nitrate(B) Bis(ethylene diamine)dithiocyanato-N cobalt(III)Nitrate(C) Bis(ethylene diamine)dithiocyanato-N cobalt(IV)Nitrate(D) Bis(ethylenediamine) dithiocyanato-N cobaltate(III)Nitrate

55. Which of the given ligand can show geometrical isomerism as well as optical isomerism in square planarhomoleptic complex.

(A) NH2

NH2

C

CCH3

CH3

CH3

CH3

(B) NH2

O

C

C

CH3

H

O

–(C)

NH2C

C

H

H

NH2H

H

(D)

NH2C

C

H

H

OO–



CHEMISTRY



(i) 1% dil. KMnO4

(ii) HIO4

C H6 12

Terminal Alkene

(i) H–Br (ii) KOH(alcoholic) (iii) O3

followedby

Zn/H O2

(D) (E)(F)

(A)

(B) + (C)

O

56. What are the products(B) and (C), respectively

(A) O

+ HCHO (B) O

+ HCHO

(C) CHO + HCHO (D) + HCHOCHO

57. What is the relationship between (A) and (E)(A) Chain isomers (B) position isomers(C) Geometrical isomers (D) Different molecular formula

58. Red Brown colour of bromine water disappears when it reacts with alkene (A) Identify the product.

(A)

Br

OH(B)

Br

OH

(C)

Br

OH(D)

Br

OH


CHEMISTRY




59. Common properties of products obtained by heating of KMnO4 and K2Cr2O7 is/are(A) Paramagnetic gas (B) Amphoteric oxide(C) Colourless gas (D) Salt does not exist in acidic medium

60. Assume molality and molarity are equal. Following solutions are equimolal aqueous solutionA : glucose B : NaCl C : BaCl2 D : Na3PO4E : Benzoic acid (weak acid)Which is/are correct statement ?(A) Boiling point A < E < B < C < D (B) Freezing point D < C < B < E < A(C) Osmotic pressure D < C < B < E < A (D) Vapour pressure of solution D < C < B < E < A


CHEMISTRY


61. Which of the following species gives gaseous product when react with NaOH. solution(A) Zn (B) NH4Cl (C) P4 (D) Pb(OH)2

62. Identify the reaction/s showing dehydration-

(A)

O

+

OH

OH

H /+ OO

(B) OHH /+

(C) O

+ H N – NH2 2H /+

N–NH2

(D) OH

H /+





0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

63. COOH

COOH(oxalic acid)

(i) C H OH(x-mole)/H2 5

(A) (i) CH –Mg Br (y )3+ – -mole

(ii) NH4

(B)

Conc. H SO2 4

(C)Cl -mole)/KOH2(z

(D)

C H O6 10 4 C H O6 14 2

C H O6 12C H O5 10 2Chloroform +

x is mole of C2H5OHy is mole of CH3–mg Brz is mole of Cl2Then, (x+y+z) is –



CHEMISTRY64. What will be the shell number of higher energy level when 96% of ionisation energy is given in ground state

to a hydrogen like specie ?

65. During electrolysis of highly concentrate H2SO4(aq), O2 (g) formed as by product.In such electrolysis 179.2 L H2(g) and 67.2 L O2(g) liberated at 1 atm and 273 K at electrodes.Calculate mol of H2S2O8 formed.

66. Find out total number of reagents which can dissolve copper turningdil. HNO3 , conc. HNO3, dil. H2SO4, conc. H2SO4, dil. HCl, conc. HCl, NaOH, H3PO4, H2CO3



CHEMISTRY67. If a solid A+B– having ZnS (zinc blende) structure is heated so that the ions along two of the axis passing

through the face centre particles are lost and bivalent ion (Z) enters here to maintain the electrical neutrality,so that the new formula unit becomes AxByZc report the value of (x + y + c).

68. A 3d unit cell is such that one of its planes has the following arrangement of atoms.

How many effective number of atoms present in a unit cell?

69. An ideal solution was prepared by dissolving some amount of cane sugar (non-volatile) in 18 g of water. Thesolution was then cooled just below its freezing temperature (270.675 K) where some ice get separated out.The remaining aqueous solution registered a vapour pressure of 735 torr at 373 K.Calculate the mass of ice separated out. (Given : Kf(H2O) = 1.86 K. kg mol–1).



CODE - ADATE : 11-10-15

B. Question paper format :9. The question paper consists of 3 parts (Mathematics, Physics and Chemistry). Each






C. Marking Scheme :
























CODE - A


DATE : 11-10-15




1. Let ABC be a fixed triangle and P be variable point in the plane of triangle ABC. Suppose a, b, c are lengthsof sides BC, CA, AB respectively. If a(PA)2 + b(PB)2 + c(PC)2 is minimum, then the point P with respect toABC, is(A) Centroid (B) Circumcentre (C) Orthocentre (D) Incentre

2. The radius of the circle which touches the line x + y = 0 at point P(–1, 1) and cuts the circlex2 + y2 + 6x – 4y + 18 = 0 orthogonally is

(A) 2 (B) 23 (C) 24 (D) 25

3. The value of )xsin(xsin2

2

1x

1–

)1–x(21–xlim

is equal to

(A) 21

e (B) 21–

e (C) 2–

e

(D) 2e

4. Given three non-zero, non coplanar vector c,b,a and cbqapr1 and cqbpar2 .

If the vectors 21 r2r and 21 rr2 are collinear, then (p, q) is

(A) (0, 0) (B) (1, –1) (C) (1, 1) (D) (–1, 1)



MATHEMATICS


5. Let A = [aij] be a 3 × 3 matrix, where x

1–)ix1(limaj1

0xij

for all 1 i, j 3. Then AA2 equals

(A) 4A (B) 3A (C) 2A (D) A

6. Let the system of equations given byx + y + z = 6x + 2y + 3z = 142x + 5y + pz = q

has infinitely many solutions, then the value of p + q is equal to(A) 44 (B) 34 (C) 24 (D) 14

7. The range of values of 'a' for which the function

3x1,x1x0,acosx–)x(f

1–3 has the smallest value at

x = 1 is(A) [cos 2, 0] (B) [–1, cos 2] (C) [0, 1] (D) [–1, 1]

8. If A is a non singular matrix satisfying A = AB – BA, then which one of the following holds true(A) det (B) = 0 (B) B = 0 (C) det (A) = 1 (D) det (B + I) = det (B – I)


MATHEMATICS




9. Which of the following limit(s) is/are equal to zero?

(A)

xx

0xx–xlim

x

(B) x1lnxlim 2

0x (C)

)1xln(

0xxlim

(D)

xtanx15–2–10lim

xxx

0x

10. If y = mx + 5 is a tangent to the curve x3y3 = ax3 + by3 at P(1, 2), then

(A) 519ba (B) a > b (C) a < b (D) 5

18ba

11. There are three coins C1, C2 and C3, C1 is a fair coin painted blue on the head side and white on the tail side.C2 and C3 are biased coins so that probability of head is 'p'. They are painted blue on tail side and red on thehead side. Two of the three coins are selected at random and tossed. If the probability that both the coins

land up with sides of the same colour is 9629

, then the possible value(s) of 'p' can be

(A) 81

(B) 83

(C) 85

(D) 87

12. If A and B are non singular matrices of same order such that AB = A and BA = B, then(A) ABA = A (B) BAB = B (C) A2 = A (D) B2 = B


MATHEMATICS





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

13. Match the equation in z, in column-I with the corresponding values of arg(z) in column-IIColumn I Column II

(A) z2 – z + 1 = 0 (P) 32–

(B) z2 + z + 1 = 0 (Q) 3–

(C) 03i1z2 2 (R) 6

(D) 03i–1z2 2 (S) 3

(T) 32


MATHEMATICS


14. Column I Column II(A) If A is a non singular matrix of order 2 such that (P) 1

A + adj(A) = A–1, then det(2A–1) equals

(B) The number of solution(s) of the equation 0sin1111cot11111

in (Q) 2

(–2, 2) is/are equal to

(C) If dt)t(tf)1–x(3dt)t(f1

x

2x

1 2

2

for all x (0, ), then

21f equals (R) 4

(D) If the area bounded between the parabolas y = 4x2 and x2 = 9y and the (S) 6

straight line y = c (c > 0) is 3

220, then c equals (T) 8


MATHEMATICS




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

15. If

2sin2sin2sin

)xsin()xsin()xsin()xcos()xcos()xcos(

)x(f ,

where , and are real constants, then find the value of

3f

6f3–

4f2 is

16. Let a and b be two vectors such 21|b||a| . If denotes the minimum value of 22 |b–a|

1|ba|

1

,

then find the number of solutions of the equation sec2 = in the interval (–4, 0).



MATHEMATICS17. In an hotel, 40% English and 60% American people are staying. English and American spellings for the

same word are 'RIGOUR' and 'RIGOR' respectively. A randomly chosen man staying in same hotel writes thisword, and a letter taken at random from his spelling was found to be a vowel. Then the propability that the

writer is an Englishmen, can be expressed as pq , p, q N and p, q are coprime then find |p – q|.

18. If 'w' is the imaginary cube root of unity, then find the number of pairs of integers (a, b) such that |aw + b| = 1.



MATHEMATICS19. Let P(x1, y1) and Q(x2, y2) be points on the parabola y = x2 – 5x + 6 at which the tangents drawn intersect at

the point R(1, 1). Find the area of triangle PQR.

20. The equation of plane which has the property that point Q(5, 4, 5) is the reflection of point P(1, 2, 3) throughthat plane is ax + by + cz = d, where a, b, c, d N. Find the least value of a + b + c.




21. In the Bernoulli’s equation

21P v gh k2

(constant) the dimensions of kP

are same as that of

(A) Thrust (B) Pressure (C) angle (D) Viscosity

22. Three point charges q1, q2 and q3 are taken such that when q1 and q2 are placed close together to form asingle point charge, the force on q3 at distance L from this combination is a repulsion of 2 unit in magnitude,when q2 and q3 are combined the force on q1 at distance L is an attractive force of magnitude 4 units. Also q3

and q1 when combined exert an attractive force on q2 of magnitude 18 unit at same distance L. The algebraicratio of charges q1q2 and q3 is(A) 1 : 2 : 3 (B) 2 : 3 : 4 (C) 4 : –3 : 1 (D) 4 : –3 : 2

23. A metallic disc of radius r is made of a material of negligible resistance and can rotate about a conductinghorizontal shaft. A smaller non conducting disc of radius a is fixed onto the same shaft and has a masslesscord wrapped around it, which is attached to a small object of mass m as shown. Two ends of a resistor ofresistance R are connected to the perimeter of the disc and to the shaft by sliding contacts. The system isthen placed into a uniform horizontal magnetic field B and the mass m is released. Find the terminal angularvelocity with which the disc will rotate finally.

(Take r = 10cm, a = 2cm , R = 1

100 , B = 0.2 T, m = 50gm, g = 10 m/s2)

m

B

r

R

B

(A) 200 rad/s (B) 300 rad/s (C) 100 rad/s (D) 10 rad/s



PHYSICS


24. Which of the following curves correctly depicts the variatin of specific heat of an ideal monatomic gas atconstant volume (CV) with temperature T.

(A)

T

3R

Cv

(B)

T

3R/2

Cv

(C)

T

Cv

(D)

T

3R/2

Cv

25. Two fixed identical metallic spheres A and B of radius R = 50 cm each are placed on a non-conducting planeat a very large distance from each other and they are connected by a coil of inductance L = 9 mH as shownin figure. One of the spheres (say A) is imparted an initial charge and the other is kept uncharged. The switchS is closed at t = 0. After what minimum time t does the charge on the first sphre decrease to half of its initialvalue ?

A BSL

(A) × 10–6 sec (B) 4

× 10–6 sec (C) 2

× 10–6 sec (D) 2 × 10–6 sec

26. A long horizontal rod has a bead which can slide along its length, the bead initially at a distance L from oneend A of the rod. The rod is set in angular motion in the horizontal plane about end A with constant angularacceleration . If the coefficient of friction between rod and the bead is , and gravity is neglected then graphbetween frictional force acting on bead and the time is :

(A)

t= / time

f

(B)

t= /2 time

f

(C)

t= / time

f

(D)

t= /2 time

f


PHYSICS


27. A rigid rod AB of length is resting on a horizontal floor. At a certain instant of time, end B has a velocity of3 m/s in the direction as shown in the figure. Minimum possible velocity of end A at this instant is :

A

B 60º3m/s

(A) 3 m/s (B) 2 m/s (C) 1.5 m/s (D) 1 m/s

28. The density vs pressure P graph of an ideal monoatomic gas undergoes a process as shown in the figure.Find the total work done during the complete process. Molecular weight of gas is M and number of moles is 1.

1 3

2

P0 3P0

0

0

(A) 0

0MP (1 – n3) (B) )3n–2(

MP

0

0 (C) )3n–3(

MP

0

0 (D) None of these


PHYSICSSECTION - II


29. The two longest wavelengths of the Balmer series of triply ionized beryllium (z = 4) are(A) 41.0 nm (B) 30.4 nm (C) 45.0 nm (D) 39.0 nm

30. The figure shows two thin large identical parallel conducting plates in air (dielectric constant = 1) with a slabof dielectric constant k placed between them. The width of the small gap between the conducting plates is dwhile the thickness of the dielectric slab is t. The conducting plates are given equal and opposite chargesdue to which the strength of the electric field in air region is E as shown. The area of plates perpendicular tothe plane of figure is A and consider it to be large. Neglect the edge effects. (The portion ABCD has the samedimensions perpendicular to the plane of the figure as that of plate or dielectric medium). Mark the correctoptions

(A) The net charge in the portion ABCD (volume) is zero

(B) The net charge in the portion ABCD (volume) is 0EAk

k

A B

CD

E

air

Con

duct

ing

plat

e

Con

duct

ing

plat

e

(C) The electrostatic energy stored in the dielectric medium is 2

0E At2k

(D) The electrostatic energy stored in the dielectric medium is 2

02

E At2k



PHYSICS


31. A uniform magnetic field B = B0 exists along x-axis. A charged particle at origin is given an initial velocityv = v0. It reaches x-axis for the first time at point P. It would have reached point P even if (assume thatparticles are projected in same direction).

(A) 2vv,

2BB 00 (B) B = 2B0, v = v0

P xO0

v0

(C) B = 2B0, v = 2v0 (D) B = B0, v = 2v0

32. A non conducting ring of radius ‘r’ has charge per unit length . The magnetic filed ‘B’ is perpendicular to theplane of the ring. The radius of the ring changes at the constant rate ‘K’. select the correct alternatives(A) Force experienced by ring is Br k(B) Force experienced by ring is zero(C) Torque experienced by ring is 2 Bkr2

(D) Torque experienced by ring is 2 Bkr2


PHYSICS





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

33. Column I gives the types of incident and emergent wave fronts respectively. Match the columnsColumn I Column-II(A) Plane, Plane (P) Convex lens(B) Plane, Spherical (Q) Concave lens(C) Spherical, Plane (R) Triangular prism(D) Spherical, Spherical (S) Plane mirror

(T) Concave mirror


PHYSICS34. Column-I contains some circuits and column-II contains some properties. In column-II current signifies

instantaneous current and potential difference refers instantaneous potnetial difference.Column-I Column-II

(A)

~

bS

R

a

x

(P) In branch x, curent varies

A closely separated conducting wire is wrapped over an insulatingcylinder. Wire is connected to a resistance R and an alternatingsource via a switch S, which is closed at t = 0

(B)

Rr

a b

S

(Q) Between points a and b,

A charged metallic sphere of radius r is earthed with a resistance potential difference decreasesR and a switch S, which is closed at t = 0. always.

(C) Sr

R

L

x

a b

An inductor L and resistor R is connected to a cell of emf and (R) In branch x, current is constantinternal resistance r with a switch(s), which is closed at t = 0

(D)

QR X

Gx J

s

a b

A circuit (used to measure an unknown resistance) is in balanced (S) Between points a and b,conditions (Galvanometer reads zero) potential difference is constant

(T) Rate of heat generation throughthe resis R is constant


PHYSICS




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

35. A uniform solid spherical ball of mass M and radius R is given an angular velocity 0 in clockwise directionand placed gently on a plank of same mass M. The friction coefficient between plank and ground is zero andbetween plank and ball is sufficient for pure rolling. The kinetic energy of the ball in Joule after long time is13K. Then find the value of K. [Assume plank is sufficiently long and M = 4.05 kg, R = 1m, 0 = 10 rad/s]

MR

0

Plank



PHYSICS36. A uniformly charged rod of charge per unit length is rotated about an axis as shown in the figure with a

constant angular velocity = 6/3). Find the magnetic moment of the system.

O

37. An ammeter and a voltmeter are connected in series to a battery of emf 6V. When a certain resistance isconnected in parallel with the voltmer, the reading of the later decreases two times, whereas the reading ofthe ammeter increases the same number of times. Find the voltmeter reading after the connection.


38. Velocity of sound in a rod is .5 × 103 ms–1 . The rod is drawn into a wire which has same volume as the rod.The wire is fixed between two supports and is just taut. When it is cooled by 30ºC, fundamental frequency oftransverse standing waves in it is 25 Hz. Find the length of the wire in m, if its coefficient of linear expansionis 3 × 10–5 ºC–1 .

39. At an instant when magnitude of source voltage is its rms value, magnitude of current is 126

times its peak

value. If the reactance is more than the resistance, determine x.

~

xmH 1

= 103

6rad s–1

40. A standing wave is set up in a string by a wave y = A sin (4x – 500 t) and its reflection (without loss ofenergy), where y, x are in metre and t is in second. P and Q are two points on the string oscillating withamplitude A. Then find the minimum distance PQ in cm. (approximate to nearst integer)


PHYSICS




41. A colourless solid X dissolves in water. The aqueous solution gives a white precipitate Y when NaOH isadded. Y dissolves in excess of NaOH but not in excess of NH4OH. Solution of ‘X’ give white precipitate withBaCl2 which are insoluble in dilute HCl. ‘X’ may be :(A) SnSO4 (B) Al2(SO4)3 (C) BeSO4 (D) All of these

42. Which of the following can act as better solvent in friedel craft alkylation of

Br

?

(A) (B)

CH3

(C)

NO2

(D)

NH2

43. The solubility of CH3COOAg would be highest in(A) acidic buffer of pH = 4 (B) basic buffer of pH = 10(C) neutral buffer of pH = 7 (D) pure water.



CHEMISTRY


44. Cl2 gas is not evolved by(A) PbO2 + conc. HCl (B) MnO–

4(aq) + HCl(C) H3PO4 + HCl (D) CaOCl2 + CO2

45. The end product of the following reactions are

O

O

CH3

(1) + NaOHI2

(2) H+

(3)

(A) yellow ppt. of CHI3,

O

COOH(B) yellow ppt of CHI3,

O

CHO

(C) yellow ppt of CHI3,

O

(D) yellow ppt of CHI3, COOHCOOH


CHEMISTRY


46. For diamond at room temperature(A) fGº = 0 , fHº < 0 , fSº < 0 (B) fGº < 0 , fHº > 0 , fSº > 0(C) fGº 0 , fHº > 0 , fSº < 0 (D) fGº = 0 , fHº < 0 , fSº > 0

47. Sn2+(aq) + Mx+(aq) Sn4+(aq) + M

M2Sx + O2(g) M + SO2

Which of the following metal satisfies above reactions(A) Ag (B) Zn (C) Hg (D) Fe

48. Orthorhombic crystal has the following unit cell parameters(A) a = b = c ; = = = 90º (B) a = b c ; = = = 90º(C) a b c ; = = = 90º (D) a = b c ; = = 90º, = 120º


CHEMISTRY




49. Select incorrect statement(s)(A) % vacant space in unit cell : FCC > BCC > SC(B) Effective no. of atoms in unit cell : SC < BCC < FCC

(C) Shortest distance between two Cl– is a2 in NaCl structure

(D) Coordination number of any cation or anion is 6 in zinc blende structure

50. Ester A (C4H8O2) + CH3MgBr (2 mole) 3(ii) H O

C4H10O (alcohol B) alcohol B reacts fastest with Lucas

reagent. Hence A and B are :

(A) CH – C – OC H , (CH ) C.OH3 2 5 3 3

O

(B) H – C – OC H , (CH ) CH.OH3 7 3 2

O

(C) CH – C – OC H , (CH ) CH.OH3 2 5 3 2

O

(D) H – C – OC H , (CH ) C.OH3 7 3 3

O


CHEMISTRY


51. Select correct statement(s)(A) A high Ea signifies that the rate constant depends strongly on temperature.(B) If a reaction has zero Ea, its rate is independent of temperature.(C) Initially heat is absorbed and finally released in nuclear fusion process.

(D) Heavy nuclei ( U23592 ) is involved in chain propogation process of nuclear fission.

52. In which of following reaction Phenol obtained as a product

(A) (1) O /h2

(2) H O3

(B) (1) NaOH/CaO/

(2) H

OH O

OH

(C) (1) KOBr

(2) NaNO /HCl2

O

NH2

C

(3) Boil. H O2

(D)

CH=O

KMnO4


CHEMISTRY





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

53. Column-I Column-IICompounds Characteristics of compounds(A) Cu2[Fe(CN)6] (P) eff = 0(B) Ag3[Fe(CN)6] (Q) Coloured due to charge transfer spectrum from metal to metal(C) BaCrO4 (R) Inner orbital species(D) [Ni(dmg)2] (S) Water insoluble

(T) Maximum four nitrogen atoms lie in a plane.


CHEMISTRY


54. Column-I Column-II(A) Acetone and benzaldehyde (P) Fehling’s solution(B) Acetaldehyde and benzaldehyde (Q) Tollen’s reagent

(C) Ph–OH

OH(R) Iodoform test

(D) Acetophenone and benzaldehyde (S) 2,4-DNP(T) FeCl3





0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

55. Metal

very dil. HNO3

conc. HNO3warm

warm No Reaction

Coloured solution + NO (g)2

excess KCN

[P] + (CN)2

Find out the value of expression |x + y| for complex compound ‘P’.Where, x = Total number of electron(s) present in Non-axial d-orbitals of central metal cation.

y = Total number of unpaired electrons present in the complex compound.

56. How many structural isomers of C4H10O react with PCC (Pyridinium chlorochromate) to give aldehyde


57. A vessel fitted with a weightless, frictionless piston of 0.025 m2, contains excess conc. Of HCl. The pistonmoved 1 m outward when 0.071 kg iron fillings were added at 300 K and 1 atm. The solution left behind was

found to contain Fe(II). Calculate the value of % purity of iron sample

10

.

58. Find out total number of acid(s) that have oxidizing character.H3BO3, HClO3 , dil. HNO3 , dil. H2SO4 H3PO4 , H4SiO4 , H2CO3 , H2S , HCl


CHEMISTRY


59. 2 SO2(g) + O2(g) 2 SO3(g)

Starting with 1.5 mol of SO2 and 1 mol O2 in 2 litre flask. After some time equilibrium established.In another experiment same mol of SO2 present at equilibrium required 500 ml 0.4 M KMnO4 in acidic

medium. Calculate the value of equilibrium constant KC for the reaction SO2(g) + 12

O2(g) SO3(g)

60. What is the value of 8Z

?

Where Z = Coordination number of 2D-square close packing+

Coordination number of 2D-hcp+

Coordination number of 3D-square close packing+

Coordination number of 3D, ABCABC ...... Packing+

Coordination number of 3D, ABAB ....... packing


CHEMISTRY



CODE - A







C. Marking Scheme :


15. For each question in Section-II, you will be awarded 4 marks if you have darkenonly the bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. No negative marks will be awarded in this Section.



DATE : 11-10-15




















CODE - A


DATE : 07-11-15




1. If f(x) = x

xxe x 3

2e 1

then f(x) is

(A) even (B) odd (C) Periodic (D) None

2.2

x 0

xlimsinx tanx

is equal to , where [ ] denotes the greatest integer function.

(A) 1 (B) 0 (C) does not exist (D) None

3. If f(x) = sin–1 2

2x1 x

then f’(2) is equal to

(A) 25

(B) 15

(C) 1

5

(D) 2

5

4. If a, b, c R such that 14a + 9b + 6c = 0 then the equation ax2 + bx + c = 0 has atleast one root in(A) (–1, 0) (B) (0, 1) (C) (1, 2) (D) None




MATHEMATICS5. If the circle x2 + y2 + 4x + 22y + c = 0 bisects the circumference of the circle x2 + y2 – 2x + 8y – d = 0

then c + d is equal to(A) 30 (B) 40 (C) 50 (D) 60

6. The number of ways in which the letters of the word MATHEMATICS can be arrange so that no two indenticalletters are together.

(A) 550 7 (B) 550 8 (C) 560 7 (D) 560 8

7. There are 10 points on a line. If 3 points are selected at randam then the probability that no two of them areconsecutive is

(A) 5

15(B)

615

(C) 7

15(D)

815

8. If 4 4sec tan 1

a b a b

, then

(A) |a| = |b| (B) |a| |b| (C) |a| |b| (D) None



MATHEMATICS9. If the median of ABC through A is perpendicular to AB then

(A) tan A + tan B = 0 (B) 2 tan A + tan B = 0(C) tan A + 2 tan B = 0 (D) none

10. If x xe cos x dx xe (sin x cos x) dx f(x) c then f(0) is equal to

(A) 0 (B) 1 (C) –1 (D) 2

11.

n

0n

0

[x] dx

{x} dx

is equal to, where n N and [x] and {x} denotes integral part and fractional part of x.

(A) n (B) n + 1 (C) n – 1 (D) None

12. If a i j k , b 4i 3j 4k

and c i j k are linearly depended vectors and | c |

= 2 then |. | is

equal to(A) 1 (B) 2 (C) 3 (D) None



MATHEMATICS13. If , m, n and + , m + m, n + n are direction cosines of two lines and is angle between them. When

is very-very small then 2 + m2 + n2 is equal to

(A) 2 (B) 122 (C) 22 (D)

14. If roots of equation ax2 + bx + c = 0 are of the form 1

and 1

, then the value of (a+b+c)2 is

(A) 2b2 – ac (B) b2 – 2ac (C) b2 – 4ac (D) 4b2 – 2ac

15. If the point P(a2 , a) lies in the region corresponding to the acute angle between the lines 2y = x and 4y = x,then(A) a (2, 4) (B) a (2, 6) (C) a (4, 6) (D) a (4, 8)

16. If a, b, c, d, e are real numbers such that 03

e6d3c210

b5a4

then the equation

ax4 + bx3 + cx2 + dx + e = 0 has atleast one real root in interval

(A) (–1, 0) (B) (0, 1) (C) (1, 2) (D) (–2, –1)



MATHEMATICS17. In a OAB, .bOBandaOA

A point P is taken on OA such that OP : PA = 3 : 1 and a point Q is taken

on OB such that OQ : QB = 1 : 2. If the lines AQ and BP are perpendicular to each other, then

(A) )b.a(15)b(9)a(4 22 (B) )b.a(36)b(9)a(4 22

(C) )b.a(15)b(4)a(9 22 (D) )b.a(36)b(4)a(9 22

18. The probability that a 2 × 2 determinant whose entries are from the set {–1, 0, 1} has value equal to–1 is :

(A) 815

(B) 8111

(C) 275

(D) 8120

19. For two non-zero vectors banda if 0b.a

then the range of bab

baa

is

(A)

3,

31

(B)

2,

21

(C)

2,

21

(D)

3,

31

20.

1k1k1kkk

k

)2–3)(2–3(6

is equal to

(A) 1 (B) 2 (C) 3 (D) 4



MATHEMATICS

21. If ,, are different from 1 and are the roots of ax3 + bx2 + cx + d = 0 and ( – ) ( – ) ( – ) = ,2

25 then

3d

)dcba(10– , where =

222

–1–1–1

is

(A) 4 (B) 5 (C) 10 (D) 12

22. The coefficients of the quadratic equation ax2 + (a + d)x + (a + 2d) = 0 are consecutive terms of a positively

valued, increasing arithmetic sequence. Determine the least integral value of ad2

such that the equation has

real solutions.(A) 10 (B) 12 (C) 14 (D) 16

23. If 22 boys are randomly divided into two teams; containing 11 boys each, then the probability that the twotallest boys are in different teams is

(A)2111

(B)74

(C)2110

(D)21

24. The value of 1.2010 + 2.2009 + 3.2008 + .............. + k. (2011 – k) ......... + 2009.2 + 2010.1 equals to

(A) 32012 C.

21

(B) 32012 C (C) 2

2012 C.2011 (D) 22011C.2012


MATHEMATICS


25. The number of values of ‘x’ for which the expression 2xx4x2x2

2

2

is a natural number

(A) 1 (B) 2 (C) 3 (D) 4

26. If lines 2x + 3y = 10 and 2x – 3y = 10 are tangents at the extremities of its same latus rectum to an ellipse

whose centre is origin, then the length of the latus rectum is

(A)27

110(B)

2798

(C)27

100(D)

27120

27. The number of increasing functions from {1, 2, 3, 4, 5} to {6, 7, 8, 9, 10} is :(A) 126 (B) 125 (C) 75 (D) 250



MATHEMATICS28. If z1 = a + ib and z2 = c + id are two complex numbers where a, b, c, d R and |z1| = |z2| = 1 and

Im 0)zz( 21 . If w1 = a + ic and w2 = b + id , then which of the following is incorrect.

(A) Im 0)ww( 21 (B) Im 0)ww( 21 (C) Im 0ww

2

1

(D) Re 0

ww

2

1

29. What are the order and degree respectively of the differential equation 0dx

yddxd

2/3–

2

2

2

2

?

(A) 1, 4 (B) 4, 2 (C) 4, 4 (D) 4, 1

30. If function f(x) = (4 sin2x – 1)n (x2 – x + 1), n N has a local minimum at 6

x , then

(A) ‘n’ can be any odd number (B) ‘n’ can be an odd prime number(C) ‘n’ can be any even number (D) ‘n’ can only be a multiple of four




31. A metallic ring of radius R moves in a vertical plane in the presence of a uniform magnetic field B perpendicularto the plane of the ring. At any given instant of time its centre of mass moves with a velocity v while ringrotates in its COM frame with angular velocity as shown in the figure. The magnitude of induced e.m.f.between points O and P is

P

O

R

B

(A) Zero (B) vBR 2 (C) vBr (D) 2 vBr

32. In the circuit shown, the capacitors C1 and C2 have capacitance C each. The switch S is closed at timet = 0. Taking Q0 = CE and = RC, the charge on C2 after time t will be

E

RC1

C2

S

(A) Q0(1 – e–t/2) (B) Q0(1 – e–t/) (C) t/20Q(1 e )

2 (D) Q0(1 – e–2t/)



PHYSICS


33. At a moment (t = 0), when the charge on capacitor C1 is zero, the switch is closed. If l0 be the current throughinductor at t = 0, for t > 0 (initially C2 is unchanged)(A) Maximum current through inductor equals l0/2

(B) Maximum current through inductor equals 1 0

1 2

C lC C

(C) Maximum charge on 1 0 21

1 2

C l LCC

C C

(D) Maximum charge on 1 1 01 2

LC C lC C

34. A point source O kept at distance of 2R from pole P of concave interfacehaving radius of curvature R emits a unidirectional beam at an angleof 30° to the principal axis PO. The distance of point of intersection ofthe ray with the principle axis from pole P is(A) 2R/3 (B) R

O

1 = 2 32 = 3

P

Interface(C) 2R / 3 (D) None of these

35. A cylinder is filled with a liquid of refractive index . The radius of thecylinder is decreasing at a constant rate K. The volume of the liquid insidethe container remains constant at V. The observer and the object O are ina state of rest and at a distance L from each other. The apparent speed ofthe object as seen by the observer, (when radius of cylinder is r)

(A) 3( – 1)2KV

( r )

(B) 2(1 )2KV

( Lr )

L

Object

Observe

(C) (1 )2K

(D) None of these


PHYSICS


36. An electron in hypothetical hydrogen atom is in its 3rd excited state and makes transition from 3rd to 2nd

excited, then to 1st excited state and then to ground state. If the amount of time spent by the electron in any

state of quantum number n, is proportional to 1

n 1

, then the ratio of no. of revolutions completed by the

elctron in 1st excited state to that in the 2nd excited state will be :

(A) 2 (B) 278 (C)

274

(D) 276

37. A parallel plate capacitor is charged to a voltage (V) by a cell and then cell is removed. Now the distancebetween the plates has to be increased by 2.4 × 10–3 m, after a 3 × 10–3 m dielectric slab is introducedbetween the plates to maintain the same initial potential difference between the plates. Find the dielectricconstant (k) of the dielectric.(A) 3 (B) 5 (C) 7 (D) 9

38. A photon of energy 10.2 eV coressponds to ligth of wavelength 0. Due to electron transition from n = 2 ton = 1 in a hydrogen atom, light of wavelength is emitted. If we take into account the recoil of atom whenphoton is emitted, then(A) = 0 (B) < 0

(C) > 0 (D) Data is not sufficient to reach a conclusion

39. An aluminium wire of cross-section 10–6 m2 is joined to a steel wire of the same cross-section lengthwise.This joint wire kept on a sonometer is pulled by a tension T = 10 kg. wt. The total length of the wire betweenthe knife edges = 1.5 m, 0.6 m of aluminium wire and 0.9 m of steel. Transverse vibrations are set up in thewire by an external force of variable frequency. What is the lowest frequency for which standing waves areformed with the joint as a node? And find the total number of nodes formed at this frequency, excluding thetwo at the knife edges. Densities of aluminium and steel are 2.6 × 103 Kg/m3 and1.04 × 104 kg/m3 respectively.(A) 162, 3 (B) 324, 6 (C) 486, 9 (D) 648, 12


PHYSICS


40. In solar radiation the the intensity of radiation is maximum around the wavelength . If R is the radius of sunand c is the velocity of light the mass lost by the sun per second is proportional to

(A) 2

4 2R

c(B)

2

2 2R

c(C)

3

4 3R

c(D)

3

4 2R

c

41. The tube shown in figure is of uniform cross-section. Liquid flows through it at a constant speed in thedirection shown by arrows. Then the liquid exerts on the tube is

(A) A net force of the right (B) A net force to the left(C) A clockwise torque (D) An anti-clockwise torque

42. The U-tube of uniform cross-section is filled with a liquid upto a height h1

and h2 in the two arms and then the liquid is allowed to move. When thelevels get equalized in the two arms, the liquid will be moving with avelocity v =

(A) 1 21 2

g(h h )2(h h h)

(B) 1 21 2

g(h h )2(h h )

h1h2

h(C) 1 2

g(h h )2h

(D) 1 2(h h ) gh


PHYSICS


43. Part of a circuit is shown in the adjoining figure. The circuit is in steady state. The energy stored in thecapacitor is (The various currents and other values are marked in the figure)

33 5

1

233V

4V

2A C

1A

1A

i1

i2

i =2A32A

C = 4 F1

(A) 2 × 10–4 J (B) 4 × 10–4 J (C) 6 × 10–4 J ` (D) 8 × 10–4 J

44. Two long straight parallel wires are 2m apart, perpendicular to the plane of the paper. The wire A carries acurrent of 9.6 A into the paper and B carries a current, the magnitude and direction of which are not known.But this current produces a magnetic field at a point P such that the total field at P = 0. The magnitude anddirection of the current through B and the magnetic field at C is

(A) 3 A, 0.7 × 10–6 T (B) 2 A, 1.7 × 10–6 T (C) 3 A, 1.3 × 10–6 T (D) 2 A, 0.7 × 10–6 T


PHYSICS


45. Two concentric coplanar circular loops have diameters 20 cm and 2 m and resistance of unit length of thewire = 10–4 /m. A time-dependent voltage V = (4 + 2.5 t) volts is applied to the larger as shown. The currentin the smaller loop is

r2

r1

V = (4 + 2.5 t)V

(A) 0.5 A (B) 0.75 A (C) 1 A (D) 1.25 A

46. A coil has self-inductance, L = 2 H. It carries current i which changes with time as i = 2sint2. What is theenergy stored in the inductance, when the current increases from 0 to 2A?(A) 2 J (B) 4 J (C) 6 J (D) 8 J

47. The magnitude of earth’s magnetic field is B0 and the angle of dip is . A horizontal conductor of length l lyingnorth-sourth moves eastwards with a velocity v. The emf induced across the rod is(A) Zero (B) B0lv (C) B0lvsin (D) B0lvcos

48. In an astronomical telescope in normal adjustment, a straight black line of length L is drawn on the objectivelens. The eye-piece forms a real image of this line. The length of the image is . The magnification oftelescope is

(A) L (B)

L 1 (C)

L 1 (D)

LL


PHYSICS


49. In a biprism experiment, calculate the intensity of light on the screen at a point 56

away from the central

image where is the fringe width. The intensity of central fringe is l0.

(A) 03I4

(B) 0I2

(C) 0I3 (D) 05I

6

50. A beam of light has three wavelengths 4144 Å, 4972 Å, 6216 Å with a total intensity of 3.6 × 10–3 W/m2

equally distributed amongst the three wavelengths. The beam falls normally on 1 cm2 of a clean metallicsurface of work function 2.3 eV. The number of photoelectrons liberated in 2s is (assume every capablephoton ejects electron)(A) 11 × 1011 (B) 8 × 1011 (C) 5 × 1011 (D) 2 × 1011

51. Two particles X and Y are initially located at distance d apart. They start moving at time t = 0. The velocity u

of Y is continuously aimed at X. At time t = 0, u is perpendicular to v

, the velocity of X. When will the

particles meet ? (Given : Magnitude of u and v

are constant)

(A) 22 v–uud

(B) 22 u–vvd

(C) vd

u–v 22(D) None of these


PHYSICS


52. When the hydrogen atom emits a photon in going from n = 5 to n = 1 state, its recoil speed is nearly(A) 10–4 m/s (B) 2 × 10–2 m/s (C) 4 m/s (D) 8 × 102 m/s

53. In a Zener diode regulator, the input voltage is 120 V and the break down voltage is 50 V. The seriesresistance is 5 k and the load is 10 k. The current through Zener diode is(A) 14 mA (B) 5 mA (C) 19 mA (D) 9 mA

54. Two small satellites move in circular orbits around the earth at distances r and r + r from the centre of theearth. Their time periods of rotation are T and T + dT (r << r; T << T). Then

(A) 3 rT T2 r

(B)

3 rT T2 r

(C)

2 rT T3 r

(D)

rT Tr



PHYSICS55. A charged dust partcle of radius 5 × 10–7 m is located in a horizontal electric field having an intensity 6.28 ×

105 V/m. The surrounding medium is air with coefficient of viscosity, = 1.6 × 10–5 N-s/m2. This particlemoves with a uniform horizontal speed (v) of 0.02 m/s, the number of electrons on the particle is(A) 10 (B) 20 (C) 30 (D) 40

56. A soap bubble of radius, r and surface tension, T is given a potential V. The relation between the new radius,R and r in terms of atmospheric pressure and T is (Assume V is final potential of the sphere)

(A) P = 4T(R2 – r2) (B) 20

1 4TP V R2 R

(C) 3 3 2 2 20

1P(R r ) 4T(R r ) V R2

(D) 04TP VRr

57. A parallel beam of light of wavelength 500 nm falls on a narrow slit and the resulting diffraction pattern isobserved on a screen 1 m away. It is observed that the first minimum is at a distance of 2.5 mm from thecentre of the screen. Find the width of the slit.(A) 0.5 mm (B) 0.3 mm (C) 0.2 mm (D) 0.1 mm



PHYSICS58. Calculate the height of the potential barrier for a head on collision of two deuterons. (Hint : The height of the

potential barrier is due to the Coulomb repulsion between the two deuterons when they just touch each other.Assume that they can be taken as hard spheres of radius 2.0 fm.)(A) 300 kev (B) 360 kev (C) 500 ev (D) 500 keV

59. A glass prism of angle A = 60° gives minimum angle of deviation = 30° with the max. error of 10 when abeam of parallel light passed through the prism during an experiment.Find the permissible error in % in the measurement of refractive index of the material of the prism.(A) 5/18 (B) 5/3 (C) 2/3 (D) 4/7

60. For transistor action, which of the following statements are correct :(A) Base, emitter and collector regions should have similar size and doping concentrations.(B) The base region must be very thick and lightly doped.(C) The emitter junction is forward biased and collector junction is reverse biased.(D) Both the emitter junction as well as the collector junction are forward biased.




61. Which species is completely dissolved in dil HCl(A) Ag2O (B) FeS (C) Pb (D) Cu

62. A compound ‘X’ on catalytic hydrogenation gives 1-methyl-3-isopropyl cyclohexane and on ozonolysisgives HCHO and the following

CHO

OCH3

O

Which of the following is compound ‘X’?

(A)

CH2

(B)

CH2

(C) CH3

(D)

CH2

63. The time of decay for a nuclear reaction is given by t = 4t1/2. The relation between the mean life (T) and timeof decay (t) is given by

(A) t = 2 T ln 2 (B) t = 4 T ln2 (C) t = 2 T4 ln 2 (D) t = 2lnT12

64. Select the CORRECT order of (Ksp) of following compounds in H2O.(A) CaCrO4 < SrCrO4 < BaCrO4 (B) Na2SO4 < Ag2SO4 < BaSO4

(C) PbS < ZnS < BaS (D) LiClO4 < NaClO4 < KClO4




CHEMISTRY

65.

OH

conc. H SO2 4

A. + H O2(major)

which of the following is product “A” in the above reaction?

(A) (B)

(C) (D)

66. Which ion has least flocculation / coagulation value for a positive sol ?(A) Cl– (B) SO4

2– (C) PO43– (D) [Fe(CN)6]4–

67. In which of the following combination product is paramagnetic species.(A) Na(s) + NH3() (B) Hot Na(s) + NH3(g)(C) ZnSO4(aq) + excess NH4OH (D) AlCl3(aq) + excess NaOH

68. When butyne is treated with aqueous H2SO4 in presence of HgSO4, the major product is(A) Butanal (B) Butanone (C) Butenol (D) Buten-2-ol



CHEMISTRY69. The enthalpy of atomisation of C6H6() is (in kJ mol–1)

[Given : B.E. (C – C) = 80 kJ mol–1 ; B.E. (C = C) = 420 kJ mol–1 ; B.E. (C – H) = 100 kJ mol–1,Resonance energy of benzene = 150 kJ mol–1 ; vapH(C6H6,) = 35 kJ mol–1](A) 1230 (B) 2215 (C) 2250 (D) 2285

70. The order of reactivity of phenyl magnesium bromide with the following compounds is(I) Acetone (II) Acetaldehyde (III) Acetophenone (IV) Benzophenone(A) I > II > III > IV (B) II > I > III > IV (C) IV > III > II > I (D) III > IV > I > II

71. Select the Incorrect matchSet of species Distinguished by using

(A) NaCl, NaBr Conc. H2SO4

(B) 2– 2–3 2 3SO , S O CaCl2

(C) Pb2+ (aq), Zn2+ (aq) Excess NH4OH(D) Ag+ (aq), Cd2+ (aq) Excess KCN

72. The enthalpy of neutralisation of strong monoprotic acid and strong monoacidic base is –57 kJ mol–1 at300 K temperature. The change in entropy of surrounding due to following reaction is (in JK–1)H+(aq) + OH–(aq) H2O()(A) 190 (B) –190 (C) 750 (D) None of these


CHEMISTRY


73. Select the correct product(s) formed on hydrolysis(A) BrF3 + H2O HOBr + 3HF (B) I2 + H2O HI + HOI(C) N2O3 + H2O HNO3 + HNO2 (D) IOF5 + H2O HIO4 + HF

74. The appropriate reagent for the following transformation

O

CH3

OH

?

OH

(A) Zn(Hg), HCl (B) H2, Ni (C) NH2–NH2, OH (D) NaBH4

75. P-V graph for liquification of three gasses are plotted at same temperature 300 K as shown below

P

V

ABC

Select the incorrect statement regarding P-V graph(A) Gas A has minimum critical temperature (B) Gas B can be liquified at 300 K(C) Gas C can be liquified at 200 K (D) Critical point of C is 300 K



CHEMISTRY76. Which metal and metal sulphide both give NO gas with dil HNO3.

(A) Zn, ZnS (B) Fe, FeS (C) Pb, PbS (D) Hg, HgS

77. Which of the following is a mismatch ?(A) Electrophoresis - movement of dispersion medium under the influence of electric field.(B) lyophilic colloids - reversible solutions.(C) Associated colloids - micelles(D) Tyndall effect - scattering of light by colloidal particles.

78. The compound that gives a positive iodoform test is(A) 1-pentanol (B) 3-pentanone (C) 2-pentanone (D) Isobutylaldehyde

79. Which of the following statement regarding H3PO3 is incorrect.(A) Its Ka value is less than H3PO2.(B) On heating it gives PH3 and H3PO4.(C) It can be prepared by hydrolysis of both PCl3 and P4O6.(D) It is formed during reaction of white phosphorous with alkali.



CHEMISTRY

80.CO/HClAlCl , 3

A conc. KOH B + C

The product B & C in above reaction respectively are :

(A) Ph – CH2OH, Ph–COOH (B) Ph – CH2OH, Ph–COO

(C) Ph – CH2O–, Ph–COOH (D) Ph – CH2O–, Ph–COO–

81. Sodium (Na = 23) crystallizes in BCC arrangement. If the unoccupied edge length of sodium crystal is

53.6 pm, then density of sodium crystal is :

(A) 2.07 g/cc (B) 1.19 g/cc (C) 2.38 g/cc (D) 0.59 g/cc

82. XeF6 undergoes partially and completely Hydrolysis and gives different Xenon compounds,select the CORRECT statement regarding Xenon compounds formed on Hydrolysis.(A) All have planer geometry.(B) All are oxo-flouro xenon compounds.(C) All are non planer and polar.(D) All have different hybridisation and different number of lone pairs on central atom.

83. Which of the following reagent can not be used to prepare cumene?

(A) + Cl AlCl3 (B) + H

(C) + FeCl3Cl(D) + H

OH



CHEMISTRY84. Potential difference of the electrical double layer formed in a colloidal sol is called

(A) Electro kinetic potential (B) EMF(C) Brownian potential (D) Electrophoresis potential

85. (i) O2

(ii) H (A)(i) NaOH, CO2

(ii) H (B) (C)Ac O2

H ,

The product C in the above reaction is

(A)

OHC–OMeO

(B)

OHC–OPhO

(C)

O–C–CH3

COOH

O

(D)

OHC–O H3–C–C

O O

86. The freezing point of equimolal aqueous solution will be minimum for(A) BaCl2 (B) NaCl (C) K4[Fe(CN)6] (D) NH2CONH2



CHEMISTRY87. Select the CORRECT order of property regarding p-block elements.

(A) B > Al > Ga > In > T (Ionisation Enthalpy).(B) CO2 < SiO2 < GeO2 < SnO2 < PbO2 (Acidic Nature).(C) NH3 < PH3 < AsH3 < SbH3 (Reducing Character).(D) F2 > Cl2 > Br2 > I2 (Bond Dissociation Energy).

88. Which of the following has weaker oxidising agent than –4MnO / H

(A) NaBiO3 / H+ (B) 2–2 8S O / H+ (C) – –

4MnO / OH (D) PbO2 / H+

89. Calculate pH of solution in anodic compartment for given cell.Pt | H2(g)| H+(aq) | | CH3COOH (aq)| H2(g) | Pt 1 bar 0.2 M 1 bar(Given : Ka (CH3COOH) = 2 × 10–5 , Ecell of reaction is 0.118 V)(A) 4.7 (B) 3.7 (C) 4.3 (D) 5.3

90. Which of the given polymer is condensation polymer as well as Homopolymer?(A) Nylon-6, 6 (B) Nylon-6 (C) Dacron (D) Glyptal




C. Marking Scheme :



CODE - ADATE : 07-11-15

date : 19-04-15 vibrant academy

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