JEE-Adv Grand Test Question Paper (P 1) - 12-05-2014

IIT Section

Subject Topic Grand Test – Paper I Date

C + M + P Grand Test – 08 IIT – GT – 08

12th May 2014 I20140508

Max. Marks: 252 Duration: 3 Hrs

1. This paper consists of 84 questions with 3 parts of Chemistry, Mathematics and Physics

Each Part consist of 4 sections

Section – I : 8 Multiple Choice Questions with one correct answer (with negative marks). A

correct answer carries 3 Marks. A wrong answer carries a penalty of 1 mark

Section – II : 5 Multiple Choice Questions with one or more correct answers (No negative

marks). A correct answer carries 3 Marks.

Section – III : 5 Comprehension Type questions. A correct answer carries 3 Marks. A wrong

answer carries a penalty of 1 mark

Section – IV : 10 Integer Type question with one correct answer. A correct answer carries 3

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 3 marks. A wrong

answer carries a penalty of 1 mark 8 x 3 = 24

1. Identify the final product obtained in the following reaction.

(a) (b)

(c) (d)

O

O

O

O

OO

O

O

O

O

O

O

O

O

O

O

O

COOC2H5

O

1)NaH2)HCHO

X ; X is

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2. The product formed in the reaction is

DHO

. OH18

H+

(a) (b)

(c) (d)

3. When sulphur is heated with aqueous NaOH , the compounds formed are

(a) 2 2Na S H O (b) 2 3 2Na SO H O

(c) 2 2 2 3 2Na S Na S O H O (d) 2 2 3 2Na S O H O

4. 2 .Zn

Ag S NaCN X Y If Y is a metal, then X and Y are respectively.

(a) 2 4,Na Zn CN Zn

(b) 2

,Na Ag CN Ag

(c) 2 4,Na Ag CN Ag

(d) 3 4,Na Ag CN Ag

. D

O18 O

.

O

.

18O

D.

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5. A reaction proceeds at a rate five times more at 60 C than it does at 30 C . Then the energy of

activation is approximately

(a) 110.8K cal mol (b) 111.8K cal mol (c) 19.8K cal mol (d) 112.8K cal mol

6. A 500 0.01ml M aqueous solution of 3 2CH NH (methanamine) is titrated by a 0.005 M HCl solution at

25 C , bK of 3 2CH NH , at 25 C is 44 10 . Then, the pH of the solution at the equivalence point is

nearly

(a) 3.5 (b) 6.5 (c) 7.5 (d) 7

7. An endothermic reaction with high activation energy for the forward reaction is given by the

diagram:

R

P

Reaction coordinate

Potentialenergy

R

R R

P P

P

Reaction coordinate

Reaction coordinate Reaction coordinate

Potentialenergy

Potentialenergy

Potentialenergy

(a) (b)

(c) (d)

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8. Which of the following volume V , temperature T plots represents the behaviour of an ideal gas

at one atmospheric pressure?

(a) (b)

(c) (d)

Section II

Multiple Choice Questions with one or more correct answer. A correct answer carries 3 marks.

No negative mark 5 x 3 = 15

9. Identify correct statement (s) for the following reaction sequence

(a) The final product is a monohydric alcohol

(b) Same carbocation intermediate is formed in both the reactions

(c) Different carbocation intermediates are formed in two reactions

(d) The final product is a polyhydric alcohol

(36.8 L at 372K)

(22.4L

at 273K)

V(L)

T(K)

(28.6L at 373K)

(22.4L

at 273K)

T(K)

V(L)

(30.6L at 373K)

(22.4L

at 273K)

V(L)

T(K)

(14.2L at 373K)

(22.4L

at 273K)

V(L)

T(K)

HN

CF3

Cl

HBr H2OA B

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10. The product(s) obtained in the following trifluoro acetolysis of given labelled phenethyl tosylate,

HH

DD

OTs

CF3COOH

?

(a) (b)

(c) (d)

11. Which of the following pairs are separable by using 4NH OH aq in excess ?

(a) 2 3,Zn Bi (b) 2 3,Sn Fe (c) 3 2, FeFe (d) 2 2, NiCr

12. In Mond’s process for the extraction of Nickel metal, a Nickel carbonyl complex is formed.

Hybridisation of Nickel in that complex is

(a) 3sp (b) 2sp (c) 2dsp (d) 2 3d sp

13. Radium has atomic mass 226 and half-life of 1600 years. The number of disintegrations per second

per gram are:

(a) 104.8 10 (b) 83.7 10 (c) 69.2 10 (d) 103.7 10

HH

DD

O CF3

O

DD

HH

O

CF3

DD

HH

O CF3

O

HH

DD

CF3

O

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Section III

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

penalty of 1 mark 5 x 3 = 15

Comprehension – I

A leaving group in an alkylating agent can be displaced not only by a nucleophile added to the reaction

mixture but also by one in the alkylating agent itself. This holds for alkylating agents that contain a

nucleophilic electron pair at a suitable distance from the leaving group. This neighbouring group

displaces the leaving group stereoselectively through backside attack and this attack corresponds to that

of an SN2 reaction. The nucleophilic electron pairs of the neighbouring group can be non-bonding, or

they can be in a bond. The higher rate of reversal substitution reactions are explained using this

neighbouring group participation.

14. S 2 chloro- 3 -ethyl- 3 -pentanol undergoes 2NS hydrolysis with aq. KOH to give

(a) S 3 ethylpentane 2,3 - diol

(b) R 3 ethylpentane 2,3 diol

(c) 2R,3R 3 methylpentane 2,3 diol

(d) 2S,3S 3 .methylpentane 2,3 diol

15. The major product obtained in the following reaction is

|

3

.2 25H C S CH CH Cl

CH

aq KOH

(a) |

3

2 25H C S CH CH OH

CH

(b) |

3

2 25H C S CH CH OH

CH

(c) 5 2 3 2C S C CH OHH (d) 5 2 3C S CH CH CHH

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16. The major product obtained in the given reaction is

EtN .

Et Cl

OH

2H O?

(a)

(b)

(c) (d)

Comprehension – II

When the solute undergoes dissociation or association in solution, the number of particles in solution

increases or decreases and thus, the colligative property changes accordingly. The extent of dissociation

or association of the solute in solution can be expressed in terms of Van’t Hoff factor, i.

In case of dissociation, 1i

1 1

1

ni

Similarly in case of association, 1i

11 1

1

ni

EtN .

Et OH

Et

N

Et

OH

.

EtN

.

Et OH

.

.Et

NOH

Et

. .

.

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17. For the solution of benzoic acid in benzene is calculated using the expression

( is the degree of dissociation or association)

(a) 1

1

i

n

(b)

1

11

i

n

(c) 1

1

i

n

(d)

1

1

i

in

18. Which of the following solutions will exhibit highest boiling point

(a) 2 40.01 M Na SO (b) 30.01M KNO (c) 0.015 M urea (d) 0.015 M glucose

Section IV

Integer answers type questions. Each carries 3 marks. No negative marks 10 x 3= 30

19. At equimolar concentrations of 2Fe and 3Fe , what must Ag

be so that the voltage of the

galvanic cell made from /Ag Ag and electrodes equals zero? The reaction is

2 3Fe Ag Fe Ag . Determine the equilibrium constant at 25 C for the reaction. (Given:

0

/0.799

Ag AgE volt

and

3 20

/0.771

Fe FeE volt

)

20. 0.789g of crystalline barium hydroxide is dissolved water. For the neutralisation of this solution.

20mL of 34

NHNO is required. How many molecules of water are present in one g mole of this base?

137.4, 16, 14, 1Ba O N H

21. A current of 2amp when passed for 5 hour through a molten salt deposits 22.2g of metal of atomic

mass 177 . The positive oxidation state of the metal in the metal salt is:

22. The dissociation constant of a substituted benzoic acid at 25 C is 41 10 . The pH of a 0.01M

solution of its sodium salt is:

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23. At 400K , the root mean square (rms) speed of gas X (molecular mass 40 ) is equal to the most

probable speed of gas Y at 60K . The molecular mass of the gas Y is

24. For a liquid the vapour pressure is given by: 10400

log 10PT

. Vapour pressure of the liquid is

10x mm Hg . The value of x will be

25. 2 2SO Cl and 2Cl are introduced into a 3L vessel. Partial pressure of 2 2SO Cl and 2Cl at equilibrium

are 1atm and 2atm respectively, the value of pK for the following reaction is10 .

2 2 2 2SO Cl g SO g Cl g . The total pressure in atm at equilibrium would be

26. Nitrobenzene 6 5 2C H NO can be reduced to aniline 6 5 2C H NH by electrolytic reduction; the

equivalent mass of nitrobenzene will be equal to molecular mass

n

. The value of n is

27. 1.2kg ethylene lycol was added in a car radiator containing 9 litre water.

The freezing of water was just prevented when car was running in the Himalayan valley at

temperature 4 C . Sudden thunderstorm in the valley lowered the temperature to 6 C . Calculate

the amount of ice separated.

28. At 10 C , the osmotic pressure of urea solution is 500mm . The solution is diluted and the

temperature is raised to 25 C , when the osmotic pressure has to be 105.3mm . Determine extent of

dilution.

CH2OH

CH2OH

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Mathematics

Section I



29. The area of the triangle formed by the complex numbers , ,z iz z iz in the Argand plane is

(a) 21

2z (b)

2z (c)

23

2z (d) none of these

30. If the line 3y x intersects the curve 21 2y x in exactly one point, then belongs to

(a) 2 (b) 2 (c) 2, 2 (d) 1

31. A triangle is constructed by joining the vertices of a regular polygon of 10 sides. The number of

ways in which this can be done so that no side of the triangle coincides with a side of the polygon is

(a) 45 (b) 50 (c) 10 (d) 120

32. Let

1sin , 0

0 , 0

nx xf x x

x .

Then f x is continuous but not differentiable at 0x , if

(a) 0, 1n (b) 1,n (c) , 0n (d) 0n

33. The area of the triangle formed by the positive x axis, the normal and tangent to the circle

2 2 4x y at the point 1, 3 is

(a) 3 sq. units (b) 2 3 sq. units (c) 4 3 sq. units (d) none of these

34. A ray of light coming from the point 1, 2 is reflected at a point A on x axis and then passes

through the point 5, 3 . The coordinates of the point A are

(a)

13, 0

5 (b)

5, 0

13 (c) 7, 0 (d) none of these

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35. The length of latus rectum of the parabola whose parametric equations are

2 21, 1,x t t y t t where t R , is equal to

(a) 2 (b) 4 (c) 8 (d) none of these

36. The equation cos2 sin 2 7x a x a possesses a solution for

(a) all a (b) 6a (c) 2a (d) 2, 6a

Section II



37. If , , a b c are in H.P, then the value of 1 1 1 1 1 1

b c a c a b

is

(a) 2

2 1

bc b (b)

2 2

1 3 2 1

4 cac a

(c)

2

3 2

abb (d) none of these

38. If n is a positive integer and 2 1

3 3 5n

, where is an integer and 0 1, then

(a) is an even integer

(b) 2

is divisible by 2 12 n

(c) the integer just less than 2 1

3 3 5n

is divisible by 3

(d) is divisible by 10

39. A bag contains four tickets marked with 112, 121, 211 and 222 . One ticket is drawn at random

from the bag. Let 1, 2, 3iE i denote the event that the thi digit on the ticket is 2 . Then

(a) 1E and 2E are independent (b) 2E and 3E are independent

(c) 3E and 1E are independent (d) 1 2 3, , E E E are independent

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40. A parallelogram is constructed on the vector 3 , 3a b .

If 2

and angle

between and is

3

, then the length of the diagonal of the parallelogram is

(a) 4 5 (b) 4 3 (c) 4 7 (d) none of these

41. If 2 3 2 3

1 1 2 2

1 2 3 4

0 0 1 1

2 , 2 , 2 and 2x x x xI dx I dx I dx I dx , then

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

Section III



Comprehension – I

Let p be a prime number and n be a positive integer. If the exponent of p in !n is denoted by !PE n ,

then

2!p K

n n nE n

p p p

where 1k kp n p and x denotes integral part of x .

Every natural number n can be uniquely expressed as 31 22 3 5 , in are whole numbers.

On the basis of above information answer the following

42. The exponent of 7 in 10050C

is

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

43. The number of zeros at the end of 108! is

(b) 10 (b)13 (c) 25 (d) 26

44. The last nonzero digit in 20! must be equal to

(a) 2 (b) 4 (c) 6 (d) 8

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The differential equation corresponding to 31 21 2 3

m xm x m xy C e C e C e , where 1 2 3, , C C C are arbitrary

constants and 1 2 3, , m m m are roots of 3 7 6 0m m is

3 2

3 20, , , ,

d y d y dya b c d a b c d

dxdx dx are constants, then

45. The order and degree of the differential equation respectively are

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

46. The value of a b d

(a) 0 (b) 6 (b) 7 (d) 5

Section IV


47. If 1z and 2z are complex numbers such that

2 2 2 21 2 1 2 1 215 13 13 15z z z z z z , then the

value of must be equal to 197 k , where k

48. The coefficient of 50x in the polynomials after like terms have been collected in the expansion

1000 999 9982 10001 1 1x x x x x x is

!,

! !

mp n

n p. Then the value of 2 3m n p is

659k , where k

49. Suppose a matrix A satisfies 2 5 7 0A A I . If 5A aA bI , then the value of 2 3a b is equal to

207k , where k

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50. A polynomial f x satisfies the condition

1 1f x f f x f

x x and 10 1001f .

Then

20f is 8000k , where k

51. Let

3

2

2

1 sin,

23cos

,2

1 sin

22

xx

x

f x a x

b xx

x

If ( )f x is continuous at 2

x

, then the value of

5/31

8

b

a is

52. If cos sin , sin cosx a t t t y a t t t , and

2

2

3t

d yb

dx, then the value of 120 ab

is 1440k ,

where k

53. Let the greatest and least values of the function 3 26 9 1f x x x x on the interval 0, 2

be

and respectively. If the value of 4 8 is 313k , then k

54. If

1

1, , >0 , 1, 2, 3, 4i

i

m m im

are four distinct points on a circle, then the value of

4

1i

i

m is

equal to

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55. If the lines 1

4 6 1:

3 5 2

x y zL

and 2 : 3 2 5 0 2 3 4L x y z x y z k

are coplanar, then k is

equal to

56. If 1 1 1 3sin sin sin

2x y z

,

then the value of 3 3 3

2162500 x y z

x y z

is 2476 k . The value

of k is

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Physics

Section I



57. A liquid of density and surface tension T is filled in the tube and the tube is rotated with angular

velocity about the given axis. Contact angle is 0 . The difference in heights of liquid in two

columns is

(a)

2 2

2

l w R T

Rg

(b)

2 2 4

4

l w R T

Rg

(c)

2 2 4

2

l w R T

Rg

(d)

2 2l w R

Rg

58. A particle of mass ' 'm is attached to a massless spring of initial length 0 '' L and spring constant ''K .

Now it is rotated in a horizontal plane with an angular velocity ' ' by fixing its other end. The

tension in the spring is given by

(a) 2

02

m KL

K m

(b)

2

20

K m

m KL

(c)

202

m KL

K m

(d)

2

20

K m

m KL

59. A capacitor ' 'C is connected to a conducting rod of length

l the loop starts entering a transverse magnetic field ' 'B as

shown in diagram, when the loop is entering the field,

what will be the charge developed across the capacitor?

(a) zero (b) BlvC (c) 2

BlvC (d)

3

BlvC

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60. If at 0t the switch wS is closed, then the charge on capacitor in the given circuit (initially

uncharged) when the current through battery becomes 50% of its

maximum value is (assume battery is ideal)

(a) 3

CE (b)

2

CE

(c) 4

CE (d) CE

61. Starting from one corner of a cube an insect has to travel to the diagonally opposite corner. The

insect travels along the edges. It traverses the first edge AB with constant velocity 1V , the second

edge BC with constant velocity 2V and the third edge CD with constant velocity

3V . The average

velocity of the whole path.

(a)

1 2 3

3

1 1 1

V V V

(b) 1 2 3

3

V V V

(c)

1 2 3

3

1 1 1

V V V

(d)

1 2 3

2

1 1 1

V V V

62. In a series LCR circuit, as the frequency of the voltage source increases, the magnitude of phase

difference between current and voltage.

(a) increases

(b) decreases

(c) first decreases, then becomes zero at a particular frequency, then increases

(d) remains constant

63. One mole of an ideal monoatomic gas undergoes process 2T V and temperature of gas changes

from 300 K to 1200 K . Then Work done by the gas is ( R is universal gas constant)

(a) 400 R (b) 450 R (c) 900 R (d) 600 R

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64. A block of mass ' 'm is being pulled up the rough incline by an agent delivering constant power p .

The coefficient of friction between the block and the incline during the course of ascent is

(a)

sin cos

pv

mg mg

(b) sin cos

pv

mg mg

(c) 2

sin cos

pv

mg mg

(d) 3

sin cos

pv

mg mg

Section II



65. A positively charged ring having uniform charge density is

shown in the figure. Two elements of ring of length 1l and

2l

subtend same angle (very small)at a point A point A is in the

plane of ring but not at the centre. The elements 1l and

2l are

at distance 1r and

2r respectively from the point A

(a) The ratio of charges of elements 1l and

2l is 1

2

r

r

(b) Net electric field at point is zero

(c) The elements 1l and

2l produce same potential at A

(d) The direction of net electric field at A towards 2l

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66. A bent conducting rod ( )PQR PQ QR l is rotating about its end P , with equal speed ω in a

region of transverse magnetic field of strength B

(a) emf induced across the rod is 2

2

Bwl

(b) emf induced across the rod is 2

8

Bwl

(c) Potential difference between points Q and R on the rod is 2

2

Bwl

(d) Electric field from P to Q is 8

Bwl

67. In an organ pipe (which may be closed or open) of 99cm length, standing wave is set up whose

equation is given by longitudinal displacement.

0.3X mm cos 2 / 0.8 0.01 ] cos 400z m t

Where z measured from the top of tube in meters and t is in

seconds.

Take end correction 1 cm choose the correct statements

(a) The upper end and lower end of tube are open and closed respectively

(b) The upper end and lower end of tube are closed and open respectively

(c) The air column is vibrating in third harmonic

(d) The air column is vibrating in second overtone

68. The path of a ray is shown in the figure. It could be the path of a wave whose

(a) Velocity in water is less than velocity in air

(b) Velocity in air is less than velocity in water

(c) Frequency does not change

(d) Wave length changes

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69. A particle excretes S.H.M according to sinx A t . The time taken by it to move from 0x to

2x A is 1T and from 2x A to 2x A is

2T then

(a) 1 2 T T (b)

1 2 T T (c) 1 22 T T (d)

2 1 2 T T

Section III



Comprehension – I

A ring of mass m and radius R rests in equilibrium on a smooth cone of semi vertical angle 45 as

shown. The radius of the cone is 2R , the radius of circular cross section of the ring is r r R

Answer the following questions

70. What will be the tension in the ring?

(a) 2 2

mg

(b)

2

mg

(c) 2

mg

(d)

2 mg

71. What will be the speed of transverse wave on the ring

(a) gR (b) 2gR (c) 1

2gR (d) 2 gR

72. If the cone is rotated about its axis with angular velocity ω. what will be the tension in the ring now ?

(a) 2( )2

mg w R

(b) 2( )

2

mg w R

(c) / 2mg (d) 2mgw R

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When a progressive wave enters from one medium to another medium, some of its energy gets

transmitted and the remaining of its energy reflected at the boundary of separation.

The energy of incident wave = The energy of reflected wave + The energy of transmitted wave

A progressive wave travels in a medium 1S and enters into another medium

2S in which its speed

decreases to 75% . What is the ratio of the amplitude of the

73. Reflected and the incident waves

(a) 1: 7 (b) 1:1 (c) 6 : 7 (d) 8 : 7

74. Transmitted and the incident waves

(a) 1:1 (b) 1: 7 (c) 8 : 7 (d) 6 : 7

Section IV


75. A metallic block of mass 1 kg and specific heat 1 cal gm C is connected to

three identical rods as shown in diagram. Temperature of ,A B and C are

maintained at 10 , 5C C and 3 C respectively. Find the final temperature of

1 kg block on Celsius scale. (Neglect any heat loss due to radiation)

76. A siren placed at a railway platform is emitting sound of frequency 5 KHz . A passenger sitting in a

moving train A records a frequency of 5.5 KHz while the train approaches the siren. During his

return journey in a different train B he records a frequency of 6.0 KHz while approaching the same

siren. The ratio of the velocity of train B to that of train A is?

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77. In the network of capacitor and resistances shown in figure,

steady current I enters at junction (a) and same current leaves

junction (b) charge on capacitor 3C with shown polarity is

4

KIRCfind K . Initially all capacitors were uncharged

78. The capacitor is charged by closing the switch ' '.S The switch is then opened and the capacitor is

allowed to discharge. 1t and

2t be the time constant of

the circuit during the charging and discharging of the

capacitor( 1 2 3R R R R ).

If the ratio of 1

2 1

t n

t n

, then the value of n is?

79. In double slit experiment, the slits are 0.5 mm apart and interference is observed on a screen placed

at a distance of 100cm from slits. It is found that 9th bright fringe is at a distance of 8.835 mm from

the 2nd dark fringe from the centre of fringe pattern. If the wavelength of light used is 73.398 10n m

then ?n

80. A single electron orbits a stationary nucleus of charge Ze where Z is a constant and e is the

magnitude of the electronic charge. It acquires 47.2 eV to excite the electron from the second Bohr

orbit to third Bohr orbit. Find the value of Z .

81. Potential difference C BV V in volts is

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82. A mono chromatic light is just able to ionise a hypothetical one electron atom in its ground state

having energy levels defined by2

17nE

n

eV where n is principal quantum number. In an

experimental set-up same light is incidents on a metal plate and it was found out that electrons have

2eV as maximum kinetic energy. If the work function of metal is 5K eV. Find the value of K.

83. Three metallic blocks A, B and C have same specific heats and

masses m, 2m and 2m respectively. Initial temperatures of A, B and

C are 10 , 5C C and 5 C respectively. Now the 3 blocks are

connected by 3 identical rod is shown. Find the final temperature of

block A on Celsius scale (neglect any heat loss due to radiation)

84. A plane concave lens is placed on a paper on which

a flower is drawn. Above its actual position does

the flower appear to be 10V cm x then find x ?

=3/2

Radius of curvature = 20cm

JEE-Adv Grand Test Question Paper (P 1) - 12-05-2014

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