JEE-Adv Grand Test Question Paper (P 1) - 10-05-2014

IIT Section

Subject Topic Grand Test – Paper I Date

C + M + P Grand Test – 07 IIT – GT – 07

10th May 2014 I20140510

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 Page 2

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. The bond angles of 3 4,NH NH and 2NH are in the order

(a) 2 3 4NH NH NH (b) 4 3 2NH NH NH

(b) 3 2 4NH NH NH (d) 3 4 2NH NH NH

2. Normal boiling point of water is 373 K. Vapour pressure of water at 298 K is 23 mm and enthalpy of

vapourisation is 40.656 kJ 1.mol If atmospheric pressure becomes 23 mm, the water will boil at

(a) 250 K (b) 298 K (c) 51.6 K (d) 12.5 K

3.

(a) (b)

(c) (d) none of these

CI

CI CI

CI

CI

CI CI

CI

CI

CI

CI CI

CI

CI

alc.KOH

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4. The equilibrium constants 1pK and

2pK for the reactions, 2X Y and Z P Q , respectively are in

the ratio of 1:9, if the degree of dissociation of X and Z be equal then ratio of total pressure at these

equilibrium is

(a) 1:36 (b) 1:1 (c) 1:3 (d) 1:9

5. Major product

(a) (b)

(c) (d)

6. When aqueous sodium hydroxide is added to an aqueous solution of chromium (III) ions, a green

blue precipitate is first formed which re-dissolves to give a green solution. This green colour is due

to

(a) 3

2 6Cr H O

(b) 2

4CrO

(c) 4

Cr OH

(d) 23 3Cr OH H O

BD3, THF

H2O2, OH18

CH3

H

D

OH

CH3

H

D

OH 18

18

OH

OH

CH3

H

CH3

H

OH

D

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7. Density of a pure substance ' 'A whose atoms pack in cubic close pack arrangement is 1 / .g cc If B

atoms can occupy tetrahedral void and if all the tetrahedral voids are occupied by ' 'B atom, what is

the density of resulting solid in /g cc ?

Atomicmass 30 / andatomicmass 50 /A g mol B g mol Z

(a) 3.33 g/cc (b) 4.333 g/cc (c) 2.33 g/cc (d) 5.33 g/cc

8. A stable molecule containing atoms of the elements ,X Y and Z has the following structure.

Which elements could be ,X Y and Z ?

X Y Z

(a) O S Cl

(b) N P Cl

(c) B C H

(d) P Si H

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. Which of the following is/are correct regarding 2C molecule?

(a) 2C molecule has been found to exist in vapour phase

(b) The total12 electrons it has, out of which 8 electrons occupy bonding orbitals while 4

electrons are anti-bonding orbitals

(c) Molecule is paramagnetic

(d) 2C molecule contains double bonds and both are bonds

X

Y

Y

X

X

Y

CH3CH3

Z

Z

Z

Z

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10. Consider the following reaction:

Which of the following are intermediate species responsible for the product?

(a) (b)

(c) (d)

11.

P and Q are

(a) (b)

(c) (d)

R CH2 COCl R CH C Cl

O

R CH C

Cl

Cl

O

R CH C Cl

OH

15 NH2

O

CH3

NH2

O

OH-, Br2

+ P + Q

NH2

CH3

15 NH2

CH3

15 NH2

NH2

R CH2 COOH Cl2/P

R CH COOH

Cl

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12. Some standard redox potentials are given below:

2

1

2Br e Br 1.07V

2 3

2 7 2

1 77 3

2 2Cr O H e Cr H O 1.33V

2

1

2Cl e Cl 1.36V

2

4 28 5 4 1.52MnO H e Mn H O V

Which of the following statements are correct under standard conditions?

(a) Bromine will oxidize chloride ions to chlorine

(b) Manganate (VII) ions in acid solution will oxidize chloride ions to chloride

(c) Manganate (VII) ions in acid solution will oxidize chromium (III) ions to dichromate (VI) ions

(d) Dichromate (VI) ions in acid solution will oxidize manganous (II) ion

13. The matsutake is a type of mushroom which is a popular element of Japanese cuisine. The spicy

aroma of this mushroom is due to methyl cinnamate, which can be prepared in the laboratory

according to the following reaction sequence:

Which reagents could be used in step I ?

(a) KCl (b) HCl (c) 5PCl (d)

2SOCl

H

COOH

H

H

COCl

H

H

COOCH3

H

Step I Step IICH3OH

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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

Consider the following process:

Reaction , /H kcal mol

Na s Na g 25.9

2

1

2Cl g Cl g 29.0 (per mole of Cl atoms)

Na g Na g e 119.9

Cl g e Cl g 86.8

2

1

2NaCl s Na g Cl g 98.2

NaCl s Na aq Cl aq 0.9

14. The heat of formation of the compound, NaCl is

(a) 0.9 / molkcal (b) 98.2 / molkcal (c) 99.1 / molkcal (d) -1 123.3 / molkcal

15. The lattice energy of ,NaCl i.e., the energy required to break up the NaCl s lettuce into Na and

Cl ions in the gaseous state is

(a) 186.2 / molkcal (b) 98.2 / molkcal (c) 185.3 / molkcal (d) 130.4 / molkcal

16. The sum of the heats of hydration of the sodium ion and chloride ion is

(a) 186.2 / molkcal (b) 0.9 / molkcal (c) 185.3 / molkcal (d) 130.4 / molkcal

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Comprehension – II

The reaction is believed to involve the attack of carbon dioxide (as electrophile) on benzene of phenoxide

ion.

Carbonylation is reversible process and ortho products predominate at 120 .C However, at 230 C the

thermodynamically more stable, para products predominate.

17.

The main product is

(a) (b) (c) (d)

COOK

OH

230oC

Product

OH OH

COOK

OH

COOK

COOH

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18. Find out the incorrect statement

(a) Carbonylation of phenoxide is an electrophilic substitution reaction

(b) Carbonylation at 120 C gives kinetically controlled product as the main product

(c) Carbonylation of phenol is catalysed by 3NaHCO as it converts phenol into phenoxide ion

(d) In carboxylation 2CO acts as an electrophile

Section IV

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

19.

Number of stereocentre in the molecule ' 'A is

20. Find iso-electric point of the given amino acid

21. The half-life period of a reaction decreases four folds when the initial concentration is increased by

two times its value. The order of the reaction is

22.

Find the number of bonds present in the molecule A .

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23. Aluminium oxide 2 3Al O is electrolysed for the production of aluminium metal. For a given

quantity of electricity if the volume of 2O gas obtained is 151.2 L measured at NTP that how many

moles of aluminium is obtained?

24. The resistance of a conductivity cell is 520when filled with 10.1mol L acetic acid and drops to

122 when NaCl is added to make the solution 0.1 1mol L in NaCl as well

(Given, : 1 2 1 1 2 1 1 2 1420 ; 126 . 91HCl NaCl NaAccm mol cm mol cm mol )

The pH of the solution is

25. When an electric current is passed through acidulated water, 112 mL of hydrogen gas at NTP is

collected at the cathode in 965 s. The current passed in ampere is

26. A sample of 10 3cm of 0.10 mol 3dm iron (II) sulphate is titrated against 0.025 mol 3dm potassium

manganite (VII) on the presence of an excess of fluoride ions. It is found that 10.0 3cm of the

manganite (VII) solution is required to reach the end point. What is the oxidation number of the

manganese at the end point ?

27. A certain mass of a substance when dissolved in 100 g 6 6 ,C H lowers the freezing point by 1.28 .C the

same mass of solute dissolved in 100g water lowers the freezing point by 1.40 .C If the substance has

normal molecular weight in benzene and is completely ionised in water, how many ions does it

dissociate in water?

1 1

2 6 61.86 and 5.12f fk H O Kmol kg k C H K mol kg

28. Total number of isomers for the molecule, 3 6C H DCl is

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Mathematics

Section I



29. ABCD is a square of side 1 unit. A circle passes through vertices A and B of the square and the

remaining two vertices of the square lie outside the circle. The length of the tangent drawn to the

circle from vertex D is 2 units. The radius of the circle is

(a) 5 (b) 1

102

(c) 1

123

(d) 8

30. The area bounded by the curves 2 1 , siny x y x and the lines 0x and 2x is

(a) 21 2cos 1 (b) 22 sin 1 (c) 2

(d) 1 log2

31. The value of

2sin

1 cos sin0

xdx

x x

is

(a) 4

(b) log 2

4

(c) log 2

4

(d) log 2

4

32. The equation of the circumcircle of a triangle ABC is 2 2 3 6 0.x y x y If

1, 2 , 3, 2A B and the vertex C varies, then the locus of the orthocentre of ABC is a

(a) straight line (b) circle (c) parabola (d) ellipse

33. A is a 3 3 matrix with entries from the set 1, 0, 1 . The probability that A is neither symmetric

nor skew-symmetric is

(a) 9 6 3

9

3 3 3 1

3

(b)

9 6 3

9

3 3 3

3

(c)

9

10

3 1

3

(d)

9 3

9

3 3 1

3

34. If 1 2, z z are complex numbers such that 3 21 1 23 2z z z and 2 3

1 2 23 11z z z , then 2 21 2z z

(a) 3 (b) 4 (c) 5 (d) 6

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35. A particle is moving along the parabola 2 12y x at the uniform rate of 10 cm/sec. Then the

component of velocity parallel to x axis when the particle is at the point 3, 6 is

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

36. Each side of triangle ABC is divided into 3 equal parts as shown in the figure. The ratio of the area

of hexagon PQRSTU to the area of the triangle ABC is

(a) 5

9 (b)

2

3

(c) 1

2 (d)

3

4

Section II



37. If 6

sin

0

x

y f x x t t dt , then the true statements among the following are

(a) 6y y x (b) 0 0y (c) 6y y x (d) 0 1y

38. If r is a vector satisfying ˆˆ ˆ ˆ ˆ2r i j k i j , then r can be

(a) (b) e (c) 1

3 (d)

1

5

39. If P is a non-singular matrix and A and B are two matrices such that 1B P AP , then the true

statements among the following are

(a) A is invertible if B is invertible

(b) 1 ,n nB P A P n N

(c) 1, B I P A I P R

( I is the identity matrix)

(d) A and B are both singular matrices

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40. If 1 2 , 0 4f x x x and 2 , 1 3g x x x , then f g x is

(a) discontinuous at 0x (b) continuous at 0x

(c) not differentiable at 0x (d) differentiable at 0x

41. Which of the following is (are) true?

(a) 300100 300 ! (b) 300300 300 ! (c) 300100 300 ! (d) 300300 300 !

Section III



Comprehension – I

A curve C which is not a straight line lies in the first quadrant. The tangent at any point on C meets the

positive directions of the coordinate axes at the points Aand B . Let d be the minimum distance of the

curve C from the origin O .

42. If 1OA OB , then d

(a) 1

2 2 (b)

1

2 (c)

1

2 (d) 2

43. If 4OA OB , then d

(a) 1

2 2 (b)

1

2 (c)

1

2 (d) 2

44. If 1AB , then d

(a) 1

2 2 (b)

1

2 (c)

1

2 (d) 2

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Let 13 15

: 55 2

y zL x

and 2

1 6:

2 5 3

x y zL

be the equations of two straight lines. A and B are

two distinct points on the x axis such that two straight lines 1 2,l l both perpendicular to the x axis

( 1l through A , 2l through B ) are drawn so as to intersect both 1 2, .L L

45. Direction ratios of one of the lines 1 2,l l are

(a) 0, 3, 1 (b) 0, 4, 3 (c) 0, 5, 2 (d) 0, 2, 3

46. If is the acute angle between the lines 1 2,l l and cos5 794

then

(a) 42 (b) 53 (c) 61 (d) 64

Section IV


47. If , , ,a b c d are non-zero numbers such that ,c d are the roots of the equation 2 0x a x b and

,a b are the roots of the equation 2 0,x c x d then the value of a b c d is

48. The value of the definite integral

1

1 1

5 2 tan sin1

tan sin tan cos2

xedx

x xe e

is

49. Suppose 4n people are seated at a round table. If three people are selected at random, and pn is

the probability that at least two of them are sitting next to each other, then 7a

pb

(when a

b is

expressed in lowest terms). The value of a b is

50. Consider a triangle ABC . The median AD meets the side BC at .D A point E on AD is chosen

such that 1 3.: :AE DE The straight line BE extended meets the side AC at the point E . Then

CF

AF equals

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51. Let 21

1

0

nnI x x dx , where n is an integer 2. Then

2

lim n

n

I

In

52. If the function 35 xf x x e and 1 ,g x f x then the value of 1g is

53. When the terms in the binomial expansion of 1 4

1

2

n

xx

are arranged in decreasing powers of

,x the coefficients of the first three terms are in arithmetic progression. The number of terms in the

expansion with integer powers of x is

54. The two circles 2 2 7 0x y px py and 2 2 10 2 1 0x y x py cut orthogonally for two

values of p : 1p and 2p . The value of 1 2p p is

55. Let 3 3 3 3

3 3 3 3

2 1 3 1 4 1 1.

2 1 3 1 4 1 1n

na

n

Then lim 3 n

na

56. Let 0

0 0A

and 50

50 .a b

A I Ac d

Then the value of a b c d is

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A

P

B

Q

C

Physics

Section I



57. A particle P is sliding down a frictionless hemispherical bowl. It

passes the point A at 0.t At this instant of time, the horizontal

component of its velocity is v . A bead Q of the same mass as P is

ejected from A at 0t along the horizontal string AB, with the

speed v . Friction between the bead and the string may be

neglected. Let pt and Qt be the respective times taken by P and Q

to reach the point B. Then

(a) P Qt t (b) P Qt t

(c) P Qt t (d) length of arc

length of chord

p

Q

t ACB

t AB

58. With what minimum speed v must a small ball should be pushed inside

a smooth vertical tube from a height h so that it may reach the top of the

tube? Radius of the tube is R

(a) 2 ( 2 )g h R (b) 5

2R

(c) (5 2 )g R h (d) 2 (2 )g R h

R

vh

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59. A bead can slide on a smooth straight wire and a

particle of mass m is attached to the bead by a light

string of length L . The particle is held in contact

with the wire with the string taut and is then let fall.

If the bead has mass 2 m . Then, when the string makes an angle with the wire bead will have

slipped a distance

(a) (1 cos )L (b) (1 cos )2

L (c) (1 cos )

4

L (d) (1 cos )

3

L

60. n moles of an ideal gas undergo a process in which the temperature changes with volume as

2T KV . The work done by the gas as the temperature changes from 0T to 04T is

(a) 03nRT (b) 0(5 / 2)nRT (c) 0(3 / 2)nRT (d) zero

61. The magnification of an object placed in front of a convex lens of focal length 20 cm is +2. To obtain

a magnification of –2, the object will have to be moved a distance equal to

(a) 10 cm (b) 20 cm (c) 30 cm (d) 40 cm

62. A hollow cylinder of specific resistance , inner

radius ,R outer radius 2R and length l is as shown

in figure. What is the net resistance between the inner

and outer surfaces?

(a) 23 R

l

(b)

2

R

(c) ln(2)2 l

(d) ln(2)

l

2m

mL

R

2R

l

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63. A circular loop of radius 1m is kept in a magnetic field of strength

2T (plane of loop is perpendicular to the direction of magnetic

field). Resistance of the loop wire is 2

/ .m A conductor of

length 2 m is sliding with a speed 1 m/s as shown in the figure.

Find the instantaneous force acting on the rod [Assume rod has

negligible resistance]

(a) 8 N (b) 16 N (c) 32 N (d) 64 N

64. Figure shows a parallel LCR circuit connected to a 200 V, AC source. L = 5H,

C = 80 F and R = 40 . At resonance let 1 2,i i and 3i be the rms current

through L, C and R. Then

(a) 1 2i i and 1 2i i (b) 1 20i i

(c) 1 2i i and 1 3i i (d) 1 2i i and 3 0i

Section II



65. A uniform rod of length 6a and mass 8m lies on a

smooth horizontal table. Two particles of mass m

and 2 ,m moving in the same horizontal plane but in

opposite directions with speeds 2v and v

respectively strike the rod normally as shown in

figure and stick to the rod. Denoting angular

velocity about the centre of mass, total energy and

translational velocity of centre of mass by , E and cv respectively, after the collision

(a) 0cv (b) 3

5

v

a (c)

5

v

a (d)

23

5

mvE

x x

x x

x x

x

x

x xx

xx

x

x

x

x

x

1 /m s

C

R

L

2m

m

2v

v

2aa

3a

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66. Three different liquids are filled in a U-tube as shown in

figure. Their densities are 1 2, and 3 respectively.

From the figure we may conclude that

(a) 2 1

(b) 1 2

(c) 3 2 12( )

(d) 2 13

2

67. Three concentric conducting spherical shells have radii ,r 2r & 3r

and charges 1 2,q q and 3q respectively. Innermost and outermost

shells are earthed as shown in figure. Select the correct alternative (s).

(a) 1 3 2q q q (b) 21

4

qq

(c) 3

1

3q

q (d) 3

2

1

3

q

q

68. In an interference arrangement similar to young’s double-slit

experiment, the slits 1S and 2S are illuminated with coherent

microwave sources, each of frequency 610 Hz. The sources are

synchronized to have zero phase difference. The slits are

separated by a distance 150.0 .d m The intensity ( )I is

measured as a function of , where is defined as shown. If 0I

is the maximum intensity, then ( )I for 0 90o is given by

(a) 0( ) / 2I I for 30 (b) 0( ) / 4I I for 90

(c) 0( )I I for 0 (d) ( )I is constant for all values of

2S

1S

d/2

d/2

1

2

3

hh

2

h

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69. A particle of charge +q and mass m moving under the influence of a

uniform electric field iE and uniform magnetic field kB follows a

trajectory from P to Q as shown in figure. The velocities at P and Q

are iv and – ˆ2vj . Which of the following statements is / are correct ?

(a) 23

4

mvE

qa

(b) Rate of work done by the electric field at P is 33

4

mv

a

(c) Rate of work done by electric field at P is zero

(d) Rate of work done by both the fields at Q is zero

Section III



Comprehension – I

70. A block is released from height ( 0)h on a rough track AB as shown in figure. Coefficient of

friction between the block and the surface is 0.5 . Track BC is smooth. From C onwards there

is a circular smooth track of radius 50R cm. For what value of h block does not leave contact

with any surface. Given 3

tan4

and 210 / .g m s

(a) 2.5h m (b) 2.0h m (c) 2.0h m (d) 1.5h m

O

P

x

v

2a

2v

Q

E

a

yB

h

A

B C

R

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71. If the block is placed on the above calculated height how many times will the block cross point C ?

(a) Infinite number of times (b) 2 times (c) 4 times (d) 3 times


Electrostatic force on a charged particle is given by .F qE If q is positive F E and if q negative

.F E

In the figure 1A Bm m kg. Block A is neutral while 1Bq C , sizes of A and B are negligible. B is

released from rest at a distance 1.8 m from A . Initially spring is neither compressed nor elongated.

72. If collision between A and B is perfectly inelastic, what is velocity of combined mass just after

collision?

(a) 6 m/s (b) 3 m/s (c) 9 m/s (d) 12 m/s

73. Equilibrium position of the combined mass is at ............ .x m

(a) 2

9 (b)

1

3 (c)

5

9 (d)

7

9

74. The amplitude of oscillation of the combined mass will be

(a) 2

3m (b)

124

3m (c)

72

3m (d)

106

9m

BA

18 /k N m

10 /E N C

smooth 0x 1.8x m x axis

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Section IV


75. A pendulum of length 1l m is released from 0 60 . The rate of change

of speed of the bob at 30o in 2/m s is 2( 10 / )g m s

76. A block of mass 2m kg is resting on a rough inclined plane of

inclination 30o as shown in figure. The coefficient of friction

between the block and the plane is 0.5. The minimum force F

in newton should be applied perpendicular to the plane on the

block, so that block does not slip on the plane is ( )x x4 2 3 . Find

x 2(Take 10 / )g m s

77. A simple pendulum has a time period 1T when it is the value of x is on the earth’s surface and 2T

when taken to a height R above the earth’s surface, where R is the radius of the earth. The value of

2 1/T T is

78. A block is kept on a rough horizontal plank. The coefficient of friction between the block and the

plank is 1/2. The plank is undergoing SHM of angular frequency 10 rad/s. The maximum

amplitude of plank in cm in which the block does not slip over the plank is 2( 10 / )g m s

79. A large tank is filled with water (density = 3 310 /kg m ). A small hole

is made at a depth 10 m below water surface. The range of water

issuing out of the hole is R on ground. Approximately what extra

pressure in atm must be applied on the water surface so that the

range becomes 2R ?

(Take 1 atm = 510 Pa and 210 /g m s )

F

30o

60o

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80. The ends of a stretched wire of length are fixed at 0x and .x L In one experiment the

displacement of the wire is 1 sin sinx

y A tL

and energy 1E and in other experiment its

displacement is 22

sin sin 2x

y A tL

and energy is 2.E Then 2

1

E

Eis

81. A ray of light falls on a transparent sphere with centre at C as shown in

figure. The ray emerges from the sphere parallel to line AB. The

refractive index of the sphere is found to be P . The value of P is?

82. A parallel combination of 0.1 M resistor and a 10 F capacitor is connected across a 1.5 V source

of negligible resistance. The time required for the capacitor to get charged upto 0.75 V is

approximately (in second)

83. At a frequency 0 the reactance of a certain capacitor equals that of a certain inductor. If the

frequency is changed to 2 0 , what is the ratio of the reactance of the inductor to that of the

capacitor?

84. The ratio between total acceleration of the electron in singly ionized helium atom and hydrogen

atom (both in ground state) is

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JEE-Adv Grand Test Question Paper (P 1) - 10-05-2014