PHYSICS

1. For a given surface the Gauss's law is stated as 0E ds .

From this we can conclude that (A) E is necessarily zero on the surface (B) E is perpendicular to the surface at every point (C) The total flux through the surface is zero (D) The flux is only going out of the surface 2. The true statement is, on increasing the distance between the

plates of a parallel plate condenser (A) The electric intensity between the plates will decrease (B) The electric intensity between the plates will increase (C) The electric intensity between the plates will remain

unchanged (D) The P.D. between the plates will decrease

3. An electric line of force in the xy plane is given by equation

2 2x y 1. A particle with unit positive charge, initially at rest

at the point x 1, y 0 in the xy plane

(A) Not move at all (B) Will move along straight line (C) Will move along the circular line of force (D) will not move on circular line of force 4. The pressure on a square plate is measured by measuring the

force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%, The maximum error in the measurement of pressure is (A) 1% (B) 2% (C) 6% (D) 8%

5. The position of a particle at time t is given by the relation

t0vx(t) (1 c ) , where 0v is a constant and 0 . The

dimensions of 0v and are respectively

(A) 0 1 1M L T and 1T (B) 0 1 0M L T and 1T

(C) 0 1 1M L T and 2LT (D) 0 1 1M L T and T

6. There are two spherical balls A and B of the same material with same surface, but the diameter of A is half that of B. If A and B are heated to the same temperature and then allowed to cool, then

(A) Rate of cooling is same in both (B) Rate of cooling of A is four times that of B (C) Rate of cooling of A is twice that of B

(D) Rate of cooling of A is 1

4 times that of B

7. P-V diagram of an ideal gas is as shown in figure. Work done

by the gas in process ABCD is

(A) 0 04P V (B) 0 02P V (C) 0 03P V (D) 0 0P V

8. An air bubble doubles its radius on raising from the bottom of water reservoir to be the surface of water in it. If the atmospheric pressure is equal to 10 m of water, the height of water in the reservoir is

(A) 10 m (B) 20 m (C) 70 m (D) 80 m 9. Latent heat of ice is 80 cal/gm. A man melts 60 g of ice by

chewing in 1 minute. His power is (A) 4800 W (B) 336 W (C) 1.33 W (D) 0.75W

10. A pipe open at both ends produces a note of frequency f1.

When the pipe is kept with 3

4th of its length it water, it

produced a note of frequency f2. The ratio 1

2

f

f is

(A) 3

4 (B)

4

3

(C)

1

2 (D) 2

11. The equation for spherical progressive wave is (where r is the

distance from the source)

(A) y asin( t kx) (B) a

y sin( t kx)r

(C) a

y sin( t kx)2

(D) a

y sin( t kx)r

v0

A F

r

= v0/2r

12. A force of 6.4 N stretches a vertical spring by 0.1 m. The mass that must be suspended from the spring so that it oscillates

with a period of 4

sec. is

(A) kg4

(B) 1kg

(C) 1

kg

(D) 10kg

13. A spherical ball of radius r and relative density 0.5 is floating in

equilibrium in water with half of it immersed in water. The work done in pushing the ball down so that whole of it is just immersed in water is : (where is the density of water)

(A) 45r g

12 (B) 0.5 rg

(C) 34r g

3 (D) 42

r g3

14. A soap bubble of radius R is blown. After heating the solution

a second bubble of radius 2R is blown. The work required to blow the second bubble in comparison to that required for the first bubble is (A) Double

(B) Slightly less than double (C) Slightly less than four times

(D) Slightly more than four times 15. A 60 kg man stands on a spring scale in the lift. At some

instant he finds, scale reading has changed from 60 kg to 50kg for a while and then comes back to the original mark. What should we conclude ? (A) The lift was in constant motion upwards (B) The lift was in constant motion downwards (C) The lift while in constant motion upwards, is stopped

suddenly (D) The lift while in constant motion downwards, is suddenly

stopped

16. A solid sphere of mass M and radius r slips on a rough horizontal plane. At some instant it has translational velocity v0

and rotational velocity about the centre v0/2r. The translational

velocity after the sphere starts pure rolling

(A) 6v0/7 in forward direction

(B) 6v0/7 in backward direction

(C) 7v0/6 in forward direction

(D) 6v0/6 in backward direction

17. A rigid body is in pure rotation, that is, undergoing fixed axis rotation. Then which of the following statement is true. (A) You can find two points in the body in a plane

perpendicular to the axis of rotation having same velocity (B) You can find two points in the body in a plane

perpendicular to the axis of rotation having same acceleration

(C) Speed of all the particles lying on the curved surface of a cylinder whose axis coincides with the axis of rotation is different

(D) Angular speed of the body is same as seen from any point in the body

18. A piece of copper and the other of germanium are cooled from

the room temperature to 80 K, then which of the following would be a correct statement (A) Resistance of each increases (B) Resistance of each decreases (C) Resistance of copper increases while that of germanium

decreases (D) Resistance of copper decreases while that of germanium

increases

19. When a 94Be atom is bombarded with particles, one of

the product of nuclear transmutation is 126C . The other is

(A) 0

1e (B) X

(C) 21D (D) 1

0n

20. Which of the following statements about the Bohr model of the

hydrogen atom is false (A) Acceleration of electron in n = 2 orbit is less than that in

n = 1 orbit (B) Angular momentum of electron in n = 2 orbit is more than

that in n = 1 orbit (C) Kinetic energy of electron in n = 2 orbit is less than that in

n = 1 orbit (D) Potential energy of electron in n = 2 orbit is less than that

in n = 1 orbit

21. X-rays are produced in X-ray tube operating at a given accelerating voltage. The wavelength of the continuous X-rays has values from

(A) 0 to (B) min to , where min 0

(C) 0 to max where max (D) min to max , where 0 < min max

22. Kinetic energy with which the electrons are emitted from the metal surface due to photoelectric effect is

(A) Independent of the intensity of illumination

(B) Independent of the frequency of light

(C) Inversely proportional to the intensity of illumination

(D) Directly proportional to the intensity of illumination

23. An ac circuit consists of an inductor of inductance 0.5 H and a

capacitor of capacitance 8 F in series. The current in the circuit is maximum when the angular frequency of ac source is

(A) 500 rad/sec (B) 2 105 rad/sec (C) 4000 rad/sec (D) 5000 rad/sec

24. The total charge induced in a conducting loop when it is moved in magnetic field depends on (A) The rate of change of magnetic flux (B) Initial magnetic flux only (C) The total change in magnetic flux (D) Final magnetic flux only

25. A conducting loop carrying a current I is placed in a uniform

magnetic field pointing into the plane of the paper as shown. The loop will have a tendency

(A) Contract (B) Expand (C) Move towards +ve x –axis (D) Move towards –ve x-axis

26. A proton (or charged particle) moving with velocity v is acted upon by electric field E and magnetic field B. The proton will move undeflected if

(A) E is perpendicular to B (B) E is parallel to v and perpendicular to B

(C) E, B and v are mutually perpendicular and E

vB

(D) E and B both are parallel to v 27. A convex lens is used to form real image of an object on a

screen. It is observed that even when the positions of the object and that screen are fixed there are two positions of the lens to form real images. If the heights of the images are 4 cm and 9 cm respectively, the height of the object is (A) 2.25 cm (B) 6.00 cm (C) 6.50 cm (D) 36.00 cm

28. In Young‟s double-slit experiment, an interference pattern is

obtained on a screen by a light of wavelength 6000 Å, coming from the coherent sources S1 and S2. At certain point P on the screen third dark fringe is formed. Then the path difference S1P – S2P in microns is (A) 0.75 (B) 1.5 (C) 3.0 (D) 4.5

29. AB is a wire of uniform resistance. The galvanometer G shows no current when the length AC = 20cm and CB = 80cm. The resistance R is equal to

(A) 2 (B) 8 (C) 20 (D) 40

30. In the given figure, when key K is opened, the reading of the

ammeter A will be

(A) 50 A (B) 2 A

(C) 0.5 A (D) A9

10

3CH

2NO

COOH

Br

3CH

2O NBr

3CH

COOH

Br

COOH

MeO 3

3

CH COONa

H OCHO X

CH CHCOOH

CHEMISTRY 31. Identify product (E) in the following sequence of reaction:

2 2Br NaNO /HClSn/HCl

Fe 273 278KA B C

2 3 2 4H O/H PO KMnO

OHD E

(A) (B)

(C) (D)

32. A dihalogen derivative „x‟ of a hydrocarbon with three carbon

atom reacts with alcoholic KOH and produces another

hydrocarbon which form red precipitate with ammonical

2 2Cu Cl „x‟ gives an aldehyde an reaction with aqueous KOH.

The compound X is:

(A) 4,3-Dichloropropane (B) 1,2-Dichloropropane

(C) 2,2-dichloropropane (D) 1,1-Dichloropropane

33. Phenol 2 2 4 2NaNO /H SO H O NaOHB C D .

Name of the above reaction is:

(A) Liebermann‟s reaction

(B) Phtholein fusion test

(C) Reimer-Tiemann reaction

(D) Schotten-baumann reaction

34.

The compound X is:

(A) 3CH COOH (B) 2BrCH COOH

(C) 3 2(CH CO) O (D) CHO COOH

2NO

KOH(solid)

2NO

OH

2NO

OH

OHOH

OHOH

35. Ethyl ester 3CH MgBr

excessP. The product P will be:

(A) (B)

(C) (D)

36.

The above reaction is:

(A) Nucleophilic substitution

(B) Electrophilic substitution

(C) Free radical substitution

(D) None of these above

37. Glyptal is:

(A) Viscose rayon (B) Nylon

(C) Polystyrene (D) Alkyd resin

38. A Zwitter ion is:

(A) A positively charged ion without metal atom in it

(B) A negatively charged ion without metal atom in it

(C) An ion with positive and negative charges at different

points in it

(D) A heavy ion with a small charge an it.

39. (i) 2 3

3S(s) O (g) SO (g) 2x Kcal

2

(ii) 2 2 3

1SO (g) O (g) SO (g) y Kcal,

2

Find out the heat of

formation of SO2 :

(A) (2x + y) (B) –(2x – y)

(C) x + y (D) 2x / y

40. The Tyndall effect is observed only when following conditions

are satisfied:

(a) The diameter of the dispersed particles is much smaller

than the wavelength of the light used.

(b) The diameter of the dispersed particle is not much smaller

than the wavelength of the light used

(c) The refractive indices of the dispersed phase and

dispersion medium are almost similar in magnitude.

(d) The refractive indices of the dispersed phase and

dispersion medium differ greatly in magnitude.

(A) (b) and (d) (B) (a) and (c)

(C) (b) and (c) (D) (a) and (d)

41. In the standardization of 2 2 3Na S O using 2 2 7K Cr O by

iodometry the equivalent weight of 2 2 7K Cr O is:

(A) Mw

2 (B)

Mw

3

(C) Mw

6 (D)

Mw

1

42. Which of the following orbitals will have zero probability of

finding the electron in yz plane:

(A) xP (B) yP

(C) zP (D) yzd

43. The type of hybrid orbital used by chlorine atom in 2ClO is:

(A) 3sp (B)

2sp

(C) sp (D) None of these

44. The osmotic pressure at o17 C of an aqueous solution

containing 1.75g of sucrose per 150 ml solution is:

(A) 0.8atm (B) 0.08atm

(C) 8.1atm (D) 9.1atm

45. The cubic unit cell of a metal (molar mass = 63.55 gm) has an

edge length of 362 pm. Its density is 8.92 g3cm. The type of

unit cell is:

(A) Primitive (B) Face centred

(C) Body centered (D) End centered

46. Volume of the air that will be expelled from a vessel of 3300cm . When it is heated from

o27 C to o37 C at the

same pressure will be:

(A) 3310cm (B)

3290cm

(C) 310cm (D)

337cm

47. A radioactive element with half life 6.5hr has 1948 10 atoms No. of atom left after 26 hr is:

(A) 1924 10 (B)

1912 10

(C) 93 10 (D)

196 10

48. 5 mole of 2SO and 5 mole of 2O are allowed to react at

equilibrium it was found that 60% of 2SO is used up. If partial

pressure of the equilibrium mixture is one atmosphere, the

partial pressure of 2O is:

(A) 0.52atm (B) 0.21atm

(C) 0.41atm (D) 0.82atm

49. What is U for the process described by figure. Heat supplied

during the process q = 100 kJ.

(A) + 50 kJ

(B) – 50 kJ

(C) –150 kJ

(D) +150 kJ

50. Activation energy of chemical reaction can be determined by:

(A) Changing concentration of reactant

(B) Evaluating rate constant of standard temperature

(C) Evaluating rate constant at two different temperature

(D) Evaluating velocities of reaction at two different

temperature

51. Aluminium oxide may be electrolysed at o1000 C to furnish

Al. The cathode reaction is: 3Al 3e Al

To prepare 5.12 kg of Al by this method would require:

(A) 75.49 10 C of electricity

(B) 71.83 10 C of electricity

(C) 45.49 10 C of electricity

(D) 15.49 10 C of electricity

52. The first ionization potential in ev of nitrogen and oxygen atom

are respectively given by:

(A) 14.6, 13.6 (B) 13.6, 14.6

(C) 13.6, 13.6 (D) 14.6, 14.6

53. In the cyanide extraction process of silver from argentite ore

the oxidizing and reducing agents used are:

(A) 2 2O & CO (B) 2O & Zn

(C) 3HNO & Zn (D) 3HNO and CO

54. Which of the following can effectively remove all type of

hardness of water:

(A) Soap (B) Washing soda

(C) slaked lime (D) None of these

55. Philospher‟s wool when heated with BaO at o1100 C gives a

compound identify the compound:

(A) 2BaZnO (B) 2Ba ZnO

(C) 2BaCdO (D) 2BaO Zn

56. Among the following compound that is both paramagnetic and

coloured is:

(A) 2 2 7K Cr O (B) 4 2 6(NH ) (TiCl )

(C) 4VOSO (D) 3 4K [Cu(NH) ]

57. The oxidation no. d-orbital occupation and coordination

number of Cr in the complex 2 2cis[Cr(en) Cl ]Cl are

respectively:

(A) +3, 3d and 4 (B) +3, 4d and 6

(C) +3, 3d and 6 (D) +2, 3d and 6

58. In the chromyl chloride test the reagent used is:

(A) 2 2 4K Cr O (B) 3CrO

(C) 2 2 7K Cr O (D) 4 2 2 7(NH ) Cr O

59. In carious method 0.099 gm organic compound give 0.287gm

AgCl. The percentage of chlorine in the compound will be:

(A) 28.6 (B) 71.7

(C) 35.4 (D) 64.2

2NH3NHCOCH

N

HN

60. Which one of the following has most nucleophilic nitrogen?

(A) (B)

(C) (D)

MATHEMATICS 61. The height of a right circular cone of maximum volume

inscribed in a sphere of diameter a is

(A) 4

a3

(B) 3

a4

(C) 2

a3

(D) 1

a4

62. Function f x 2 x 1 is not differentiable at x

(A) 1,0 (B) 0,1, 1

(C) 1,0,3 (D) 1,1,3

63. If A and B are two matrices with 32 and 40 elements respectively, then the probability that the product AB is possible is

(A) 1

18 (B)

2

18

(C) 1

12 (D)

1

14

64.

1x

x2 3

2 1 11 x e dx

x x x

is equal to

(A)

1x

x1x e C

x

(B)

1x

x1x e C

x

(C)

1x

x1x e C

x

(D)

1x

x1x e C

x

65.

50

0

sinx cos x

dx is equal to (where [.] is greatest

integer function)

(A) 15

2

(B) 50

(C) 25 (D) 0

66. The general solution of the differential equation

dy x y 1

dx 2x 2y 1

is

(A) elog 3x 3y 2 3x 6y c

(B) elog 3x 3y 2 3x 6y c

(C) elog 3x 3y 2 3x 6y c

(D) elog 3x 3y 2 3x 6y c

67. Let

2

1 60

x xI dx;

1 x

2 60

x xI dx;

1 x

then

(A) 1 2I 2I (B) 2 1I 2I

(C) 21 2I I (D) 1 2I I

68. 2 2 2 2n

1 1 1 1lim n ...

n 1 n 2 n 3 2n

(A) 1

2 (B) n2

(C) 3

2 (D) 0

69. If 1

tan1

21

22

, where 0,2 then is

(A) 7

8

(B)

8

(C) 12

(D)

5

12

70. If 1 1 1 1sin x sin y cos y cos x6

, then the number

of ordered pairs x,y is

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

71. Let S be a non empty subset of N. Negation of the statement

“There exists a number x S such that x is even” will be:

(A) There exists a number x S such that x is odd

(B) For any number x S, x is even

(C) For every number x S , x is odd

(D) None of these

72. If the statement r : p ~p q then r is logically equivalent

to

(A) p ~q p (B) p ~q ~p

(C) q p p (D) q p ~p

73. The arithmetic mean and mode of a data are 24 and 12

respectively, then the median of the data is (A) 20 (B) 18 (C) 21 (D) 22

74. A five digit number with distinct digits is formed by using the digits 0, 1, 2, 3, 4, 5. The probability that the number is divisible by 3 is

(A) 6

55

P

6 (B)

9

25

(C) 6

55

C

6 (D)

9

23

75. 2

2

3x mx nf : R R,f x

x 1

. If the range of this function is

4,3 . Then the value of m n is

(A) 4 (B) 3

(C) 7 (D) 1

76. The number of five digit numbers that contains digit 7 exactly once as (if digits may be repeated)

(A) 341 9 (B) 337 9

(C) 47 9 (D) 441 9

77. The number of 4 digit numbers of the form N abcd which

satisfy the following condition

(i) 4000 N 6000

(ii) N is divisible by 5

(iii) 3 b c 6

(If digits may be repeated)

(A) 24 (B) 20

(C) 23 (D) 25

78. Two AM‟s 1A and 2A , two GM‟s 1G & 2G and two HM‟s

1 2H & H are inserted between any two numbers then

1 11 2

H H equals

(A) 1 11 2

A A (B) 1 11 2

G G

(C) 1 2

1 2

G G

A A (D)

1 2

1 2

A A

G G

79. The number of terms in the expansion of 500

64 9 8 ,

which are integers is

(A) 501 (B) 251

(C) 42 (D) 41

80. If

3 3 4

A 2 3 4

0 1 1

then

(A) Adj Adj A I (B) Adj Adj A 1

(C) Adj A A (D) All of these

81. If i

3x i y

2 e

, then locus of P x,y will represents a /

an (A) Ellipse if 1, 2

(B) Pair of straight line if 1, 0

(C) Circle, if 1, 1

(D) All of them

82. If the points A z , B z and C 1 z are the vertices of an

equilateral triangle ABC then Re z is equal to

(A) 1

4 (B)

3

2

(C) 1

2 (D)

1

3

83. If e is the eccentricity of the hyperbola 2 2

2 2

x y1

a b & is

angle between the asymptotes, then cos2

(A) 1 e

e

(B)

1 e

e

(C) 1

e (D)

e 1

e

84. If the lines ˆ ˆ ˆ ˆ ˆr 2i j k i 2j and

ˆ ˆ ˆ ˆ ˆr i j 3k j 2k intersect each other, then is

equal to (A) 2 (B) –1 (C) 0 (D) 1

85. The volume of the tetrahedron formed by the coterminous

edges a,b,c is 3. Then the volume of the parallelopiped

formed by the coterminous edges a b, b c, c a is

(A) 6 (B) 18 (C) 36 (D) 9

86. If a vector r of magnitude 3 6 is directed along the bisector

of the angle between the vectors ˆ ˆ ˆa 7i 4j 4k and

ˆ ˆ ˆb 2i j 2k then r is

(A) ˆ ˆ ˆi 7 j 2k (B) ˆ ˆ ˆi 7 j 2k

(C) ˆ ˆ ˆi 7 j 2k (D) ˆ ˆ ˆi 7 j 2k

87. The equation of latusrectum (LR) of a parabola is x y 8

and the equation of the tangent at the vertex is x y 12 ,

then length of LR is

(A) 4 2 (B) 2 2

(C) 8 (D) 8 2

88. Maximum length of chord of the ellipse 2 2x y

18 4

, such that

eccentric angles of its extremities differ by 2

is

(A) 4 (B) 2 2

(C) 16 (D) 8

89. Let R be a relation defined on N N by

a,b R c,d a b c c a d . Then R is

(A) reflexive, symmetric (B) symmetric, transitive (C) transitive only (D) equivalence

90. The length of the sub-tangent at any point of the curve m n m nx y a is proportional to

(A) Ordinate (B) Abscissa

(C) nOrdinate (D) nAbscissa