jee-adv grand test question paper (p 2) - 14-05-2014

IIT Section

Subject Topic Grand Test – Paper II Date

C + M + P Grand Test – 09 IIT – GT – 09

14th May 2014 I20140508

Max. Marks : 237 Duration : 3 Hrs

1. This paper consists of 57 questions with 3 parts of Chemistry, Mathematics and Physics

Each Part consist of 4 Sections

Section – I : 6 Multiple Choice Questions with one correct answer (with negative marks). A

correct answer carries 5 Marks. A wrong answer carries a penalty of 2 mark

Section – II : 5 Integer type questions. A correct answer carries 3 Marks. No negative marks.

Section – III : 6 Comprehension Type questions. A correct answer carries 3 Marks. A wrong

answer carries a penalty of 1 mark

Section – IV : 2 Matrix Match type questions. A correct answer carries 8 Marks. No

negative mark.

2. Darken the appropriate bubble using a pen in the OMR sheet provided to you. Once

entered, the answer cannot be changed. Any corrections or modifications will

automatically draw a penalty of 1 mark.

3. Use of calculators and log tables is prohibited.

4. No clarification will be entertained during the examination. Doubts in the paper can be

reported to the coordinator after the exam.

All the best !!

Useful Data

At. Wt.:

N = 14; O = 16; H = 1; S = 32; Cl = 35.5; Mn = 55; Na = 23; C = 12; Ag = 108; K = 39; Fe = 56; Pb = 207

Physical constants:

346.626 10 J.sech , 23 -1

aN 6.022 10 mol , 8 -1C 2.998 10 ms , 31

em 9.1 10 kg

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Ace Insignia Rough Work

Chemistry

Section I

Multiple Choice Questions with one correct answer. A correct answer carries 5 marks. A wrong

answer carries a penalty of 2 marks 6 x 5 = 30

1. Which of the following solution will have pH close to 1.0 ?

(a) 100 /10 100 /10ml of M HCl ml of M NaOH

(b) 55 /10 45 /10ml of M HCl ml of M NaOH

(c) 10 /10 90 /10ml of M HCl ml of M NaOH

(d) 75 / 5 25 / 5ml of M HCl ml of M NaOH

2. In the given reaction the end product Y is

3CH CH COOH (a) (b)

(c) (d )

OH

2CH CH COOEt

3CH CH COOEt

OH

2CHCH CHC OEt

O O

CH2 CH2

HCN (X) (Y)

O (i) H2SO4 / H2O

(ii) EtOH / H

Al2O3

300 C

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3.

Identify the product

4. The rate law for the gaseous reaction of nitric oxide and hydrogen is

2

x ydP NOK P NO P H

dt In one series of experiments in which the initial pressure of

hydrogen was held constant, the initial decrease in the partial pressure of NO was 1200 Pa s

for 10 0

0.479 bar and 137 for 0.400 bar.P NO Pa s P NO What is the order of reaction with

respect to NO ?

(a) 0 (b) 1 (c) 2 (d) 3

CH3

NO2

NO2

OH

?H2S, NH3

50 C

(a)

(c)

(d )

(b)

CH3

NO2

NH2

OH

CH3

NH2

OH

NH2

CH3

NH2

OH

NO2 CH3

NO2

OH

NO2

NH2

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5. Two glass bulbs A and B are connected by a very small tube having a stop cock. Bulb A has a

volume of 3100cm and contained the gas while bulb B was empty. On opening the stop-cock., the

pressure fell down to 40%. The volume of the bulb B must be

(a) 375cm (b) 3125cm (c) 150cm (d) 3250cm

6. The pair in which both species have same magnetic moment (spin only values) is

(a) 2 2

2 46;Cr H O CoCl

(b) 2 2

2 26 6,Cr H O Fe H O

(c) 2 2

2 26 6,Mn H O Cr H O

(d) 22

4 2 6,CoCl Fe H O

Section II

Integer answers type questions. Each carries 3 marks. No negative marks. 5 x 3 = 15

7. An organic compound 6 12A C H O forms an oxime but does not reduce Tollen’s reagent. A on

reduction with sodium amalgam forms an alcohol B which on dehydration forms chiefly a single

alkene C . The ozonolysis of C produces D and E . The compound D reduces Tollen’s reagent

but does not answer iodoform test But E answer iodoform test but not Tollen’s reagent. The

position of double bond in compound C is

8. In alkaline medium 2ClO oxidises 2 2H O to 2H O and 2O , itself gets reduced to Cl . The

number of moles of 2 2H O oxidised by 2 moles of 2ClO is

9. The enthalpy of neutralization of 4NH OH and 3CH COOH is 10.5 /kcal mol and enthalpy of

neutralization of 3CH COOH with strong base is 12.5 / .kcal mol The enthalpy of ionisation of

4NH OH is

10. ' 'X is colourless, tasteless and odourless and does not help in combustion. ' 'X along with

2 2CO and H O can be obtained by the action of nitrous acid on an organic fertilizer. The bond

order of ' 'X is

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11. Pyrolusite on heating with KOH in presence of air gives a dark green compound A . The

solution of A on treatment with 2 4H SO gives a purple coloured compound B . KI on

reaction with alkaline solution of B changes to compound C . If A B and C contain

same transition metal atom, the number of unpaired electrons in the cation of C is

Section III

Comprehension type questions. A correct answer carries 3 marks. A wrong answer carries a

penalty of 1 mark 6 x 3 = 18

Comprehension – I

Ozonolysis (cleavage by ozone) of alkene is carried out in two stages; first, addition of ozone

to the double bond to form an ozonide; and second, hydrolysis of the ozonide to yield the cleavage

products. Ozone gas is passed into a solution of the alkene in some inert solvent like carbon

tetrachloride; evaporation of the solvent leaves the ozonide as viscous oil. This unstable, explosive

compound is not purified, but is treated directly with water, generally in the presence of a reducing

agent.

Acetylene and its homologues form ozonides with ozone and these compounds are decomposed by

water to form diketones, which are then oxidised to acids by the hydrogen peroxide formed in the

reaction

3OC C

alkene

2H O

Zn

cleavage products (aldehydes and ketones) ozonide

C O O C C

O

O

C

O

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Acetylene is exceptional. It gives glyoxal as well as formic acid

12. Which alkene on ozonolysis gives 3 2 3 3CH CH CHO and CH COCH

(a) 3 2 3 2CH CH CH C CH (b) 3 2 2 3CH CH CH CHCH CH

(c) 3 2 3CH CH CH CHCH (d) 3 32CH C CHCH

13. Ozonolysis of 7 14C H gave 2 3 tan .methyl pen one The alkene is

(a) 2-ethyl-3-methyl-1-butene (b) 3-ethyl-2-methyl-3-butene

(c) 2,5-dimethyl-3,4-dimethylhex-3-ene (d) 3-ethyl-2-methyl-1-butene

14. An Alkyne which forms two moles of acetic acid only on ozonolysis is

(a)1-butyne (b) 2-butyne (c) 3-methyl-1-butyne (d) methyl acetylene

Comprehension – II

0.16 g of methane was subjected to combustion at 27 C in a bomb calorimeter. The temperature

of the calorimeter system (including water) was found to rise by 0.5 .C The thermal capacity of the

calorimeter system is 117.7kJ K

15. The heat of combustion of methane at constant volume is

(a) 1885 kJ mol (b) 1885kJ mol (c) 1889.98 kJ mol (d) 1889.98 kJ mol

16. Fuel efficiency of 4CH is

(a) 885 kJ (b) 55.3 kJ (c) 221 kJ (d) 8.85 kJ

O O

O

1 23R C CR O

21 2 H OR C CR

1 2 1 22 2 2 2R C CR H O R CO H R CO H

O O

2

( ) 32( )

i O

ii H OCH CH OCHCHO HCO H

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17. Heat of combustion of methane at constant pressure is

(a) 1889.98kJ mol (b) 1889.98kJ mol (c) 1880.91 kJ mol (d) 1880.91kJ mol

Section IV

Matrix Match type questions (4 rows per matrix type, 2 marks per row) 2 x 8 = 16

18. Matrix Match –I

Column I Column II

(A) butter of tin (p) 3 2Pb CH COO

(B) dry ice (q) 3 22 .PbCO Pb OH

(C) sugar of lead (r) 4 2.5SnCl H O

(D) white lead (s) solid 2CO

19. Matrix Match –II

Column I Column II

(A) detergents (p) glycerides

(B) petroleum wax (q) sodium alkyl sulphonates

(C) fats (r) sodium salt of higher fatty acid

(D) soap (s) candles

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Mathematics

Section I



20. If the graph of 3 22 , f x x ax bx ab N cuts the x axis at three distinct points, then

minimum value of a b is

(a) 3 (b) 4 (c) 5 (d) 2

21. Let 1, 2, 3, , 22 .A Set B is a subset of A , and B has exactly 11 elements. The sum of

elements of all possible subset B

(a) 2111252 C (b) 21

10230 C (c) 219253 C (d) 21

10253 C

22. Let x denote the greatest integer less than or equal to .x Let 23 22sin cosf x x x and

111 tan

2g x x . Then the number of real values of x in 10 , 20

satisfying the equation

f x g x is

(a) 6 (b)10 (c)15 (d) 20

23. If z is a complex number satisfying 2

1 2z i and 2

z

, then the locus traced by in the

complex plane is

(a) 1 0x y (b) 1 0x y (c) 1 0x y (d) 1 0x y

24. The minimum value of 2 2, 4 6f x y x x y y , where 0 1x and 0 1y , is

(a) 1 (b) 2 (c) 3 (d) 5

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25. Let 6

1 iia x

and

6

1 iib y

If

61 1

1

sin cos 9 ,i i

i

x y

then 2

2log 1

1

b x

xa

ex x dx

e

is

equal to

(a) 0 (b) 6 6e e (c) 37

log12

(d) 6 6e e

Section II


26. If 4 4sin cos 2 4sin cos , 0 , 2

x y x y x y

, then sin cosx y

27. If 1

,5 2

x

then 1 1 2[ cos(cot ) sin(cot )]x x x

. Then the value of

50

51 is

28. If 5, 12 and 24, 7 are the foci of a hyperbola passing through the origin, then the eccentricity

of the hyperbola is . Then the value of 12

386

is

29. Let

2

2

1 cos

1

sin

2

t

t

I xf x x dx

and

2

2

1 cos

2

sin

2

t

t

I f x x dx

. Then 1

2

I

I is equal to

30. The remainder when 20002 is divided by 17 is

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Section III



Comprehension – I

Consider the planes 1 : 2 1P x y z , 2 : 2P x y z and 3 : 3 5P x y z .

The planes 1P and

2P intersect at a point A on the XOY plane and at a point B on the YOZ plane,

where O is the origin. 3P passes through the point A .

31. The value of is

(a) 2 (b) 7 (c) 4 (d) 5

32. The length of the projection of AB on the x axis is

(a) 1 (b) 9 (c) 8 (d) 7

33. If the coordinates of a point C situated at a minimum distance from point O on the line AB are

, , p q r , then the value of 7 14 14p q r is

(a) 1 (b) 2 (c) 3 (d) 4


The asymptotes of a rectangular hyperbola are parallel to the coordinate axis. If two perpendicular

tangents of the hyperbola intersect at 2, 2 and orthocentre of the triangle formed by any three

points on the hyperbola is 0, 0 , then

34. The equation of the conjugate hyperbola is

(a) 2 2 4x y (b) 3 3 9x y

(c) 2 2 4x y (d) 4 4 16x y

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35. A tangent to the hyperbola at 4, 4 intersects the asymptotes at points A and .B Then the

length of AB is

(a) 4 (b) 4 2 (c) 8 2 (d) 16

36. A chord whose midpoint is 4, 0 of rectangular hyperbola is a tangent of its conjugate

hyperbola then the coordinates of the point of contact is

(a) 3, 1 (b) 3, 2 3 (c) 2, 2 (d) none of these

Section IV



Let A be a square matrix of order 2 with the elements 0, 1, 2 and 4 . Let N denote the number

of such matrices.

Column – I Column – II

(A) Possible non-negative values of det A is (are) (p) 2

(B) Sum of values of determinants corresponding to the N

matrices is

(q) 4

(C) If absolute value of det A is least, then the possible values

of adj adj adj A is (are)

(r) 2

(D) If det A is algebraically least, then the possible value of

1det 16A

is

(s) 0

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If 3 2 0f x x ax bx c , has three distinct integral roots and

3 2

2 2 22 2 2 2 2 2 0x x a x x b x x c

has no real roots, then

Column – I Column – II

(A) The value of a is (p) 0

(B) The value of b is (q) 2

(C) The value of c is (r) 3

(D) If the roots of f x k are equal, then

the value of k is

(s) 1

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Physics

Section I



39. Two cars A and B starts from ' 'O simultaneously with uniform

speed V such that A is along diameter and B is along circular

path of radius R as shown in the figure. The displacement of B with

respect to A and velocity of B with respect to A after time 2

R

V

are

(a) 2 , 2Ri Rj Vi Vj (b) , 0R R i Rj V V i j

(c) 2 , 2R R i Rj Vi Vj (d) ,02

R R i Rj i

40. Specific heat capacity is the cause of formation of land and sea breeze, because

(a) The specific heat of water is more than land

(b) The specific heat of water is less than land

(c) The specific heat of air above the water is more than land

(d) The specific heat of air above the water is less than land

xO

y

R

B

A

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41. A ray of light is incident at grazing incidence at origin. X Z

plane separates two media. For 0y it is air and for 0y it is a

medium of continuously varying refractive index. If slope at a

point ,P x y on the ray is m y , then the refractive index as the

function of y is

(a) 2

1y m y (b)

2

1

1

y

m y

(c)

2

11y

m y (d)

2

11y

m y

42. In the plane mirror, the co-ordinates of image of charged

particle(initially at origin as shown) after two and half time

periods are (initial velocity 0V is in the xy -plane and the plane

of the mirror is perpendicular to the x -axis. A uniform

magnetic field ˆ B j exists in the whole space. 0P is pitch of helix,

0R is radius of helix)

(a) 0 017 , 0, 2P R (b) 0 03 , 0, 2P R (c) 0 017.5 , 0, 2P R (d) 0 03 , 0,2P R

43. A charge q is placed at the centre of a cylinder of radius R and length 2R . Then electric flux

through the curved surface of the cylinder is

(a) 2o

q (b)

4o

q (c)

2 o

q (d)

2 2 o

q

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44. A hoop of radius r and mass m is rolling without

slipping with velocity v towards a step of height

h r on a horizontal surface. Assume the hoop does

not rebound and no slipping occurs at the point of

contact when the hoop rolls up. The minimum velocity v needed for the hoop to roll up the step

is

(a) 2

r gh

r h (b) gh (c)

2

2

r gh

r h (d) 2 gh

Section II


45. A block of mass 1.8 kgm is placed on a wedge and it is

attached to the top of the inclined plane with a light string

which is parallel to the inclined plane as shown in the

figure.

If the magnitude of acceleration ' 'a of wedge is 25 m/s

6,

then the block pushes the inclined plane of the wedge with a force of 1

nmg

n newtons. (Friction

is absent everywhere). The value of n is

a

37

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46. An ideal gas is enclosed in a cylinder fitted with a

frictionless piston. The piston is connected with a light

rod to one plate of capacitor whose other plate is fixed as

shown. Initially volume of the gas inside the cylinder is

0V . Atmospheric pressure is

0P , separation between the

plates is L , area of the piston as well as of the capacitor plates is A and emf of battery is . A

heater supplies heat to the gas so that pressure of the gas is given as

2

0

20,

nP P

L

when piston

is displaced by a distance 2

L. Find value of n .

47. Heat is generated uniformly per unit volume inside a spherical volume of radius 1m at rate of

320 /W m . The thermal conductivity of the spherical volume in 1

/6

W mK . If the outer surface

temperature of the sphere is 020 C and if the temperature of the centre of the sphere is 10x (in

degree centigrade), find x .

48. The radius of curvature of each surface of an equi convex lens is 42R cm . Refractive index of

the glass 1.25 . If the final image forms after four internal reflections inside the lens (for

paraxial incident beam ) Calculate the distance of the image from the lens in cm .

49. A wall is moving with velocity u and a source of sound moves with

velocity / 2u in the same direction as shown in the figure. If the sound

travels with velocity 10 ,u then the ratio of incident sound wavelength

on the wall to the reflected sound wavelength by the wall would be

: 2X X . The value of X is

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Section III



Comprehension – I

Three cells with emf’s 1 , 2 &3V V V and each having an

internal resistance 1 are connected to an external

resistance 4R as shown in the circuit.

50. The effective emf of the three cells is

(a) 6V (b) 3V (c) 2V (d)1V

51. Current passing through 2V cell is

(a) 6

39A (b)

6

7A (c)

3

2A (d)

4

13A

52. If 2V cell is reversely connected, then the current passing through ' 'R is

(a) 8

13 (b)

6

13A (c)

4

13 (d)

2

13A


A particle of mass m has to move along the curved

path (as shown in figure) O a b c d , in a horizontal

plane whose radius is decreasing as shown in figure

2V

1V

3V

4R

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53. If the particle moves with constant speed v then the magnitude of acceleration Vs time graph will

be

(a) (b)

(c) (d)

54. If the particle moves under constant centripetal acceleration (in magnitude) then speed Vs time

graph will be

(a) (b)

(c) (d)

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55. Let the particle at rest at time 0t at point O when an impulse provides a velocity ˆvk to it now

further particle moves over the curved path with constant acceleration (in magnitude) ‘ k ’ then

the sum of impulse received by it at a,b,c,d ..... (i.e. at the end of semicircle) over the entire path

(excluding impulse given at O ) must be

(a) 3

m kr (b) m kr (c) 3m kr (d)

3

2m kr

Section IV



An object is starts moving from infinity along the principle axis of a convex lens. If

F is focus of the lens

C is centre of curative of the lens

P is pole of the lens

Then match the position of object in Column I with nature of image in Column II

Column I Column II

(A) At infinity (p) virtual and enlarged

(B) At F (q) real and enlarged

(C) Between F & P (r) inverted

(D) Between C & F (s) erected

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A conducting rod shown in fig. of mass m and length L moves on two frictionless parallel rails

in the presence of uniform magnetic field directed into the page. X is load connected between

parallel rails. The rod is given an initial velocity 0v to the right and released at 0t . Match Col-I

with Col-II

Column I

Column II

(A)

If X is the resistance of resistance R

(p)

Rod moves under the action of

magnetic force

(B) If X is a solenoid of negligible

resistance

(q) Energy is conserved

(C)

If X is the capacitor of capacitance C

and conducting rod is dragged by a

constant force 0F

(r) Velocity of rod increases linearly with

time

(D)

If X is a capacitor of capacitance C

and the arrangement are fixed

vertically and conductor is released

from rest.

(s) Rod oscillate simple harmonically

jee-adv grand test question paper (p 2) - 14-05-2014

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