exam_paper_22.12.2013

8/12/2019 Exam_Paper_22.12.2013

1/13A-49, Maulana Azad Sarani, City Centre, Durgapur-16, (WB) Call-7699999929

Response @ www.iitjeeguru.in

1. A particle is in uniform circular motion in a horizontal plane. Its angular momentum is constant when

the origin is taken at :(A) centre of the circle (B) any point on the circumference of the circle(C) any point inside the circle (D) any point outside the circle

2. Two particles, each of mass M, are connected a rod of negligible massand length L. The system is lying on a horizontal frictionless surface. An

impulse Mv, perpendicular to the rod, is given at one end of the rod asshown in the figure. The angular velocity acquired by the rod is

(A)L

v4 (B)L

v2(C)

L

v(D)

L4

v

3. A platform is revolving in horizontal plane about a fixed axis and a boy issitting at centre. The initial kinetic energy of system is K. If the boy stretches

his arms then moment of inertia of system becomes double. Final kinetic energy of system is :

(A) K (B)2

K(C)

4

K(D) 2K

4. A disc is moving without slipping on ground then the relation between magnitudeof velocity of points P, C and Q is [distance CP = CQ]

(A) Q > C > P (B) P > C > Q(C) C > Q > P (D) All will be same

5. A block of mass m is held fixed against a wall by a applying a horizontal

force F. Which of the following option is incorrect.

(A) friction force = mg (B) normal will not produce torque(C) F will not produce torque (D) normal reaction = F

6. A disc has mass 9m. A hole of radius3

Ris cut from it as shown in the figure.

The moment of inertia of the remaining part about an axis passing through thecentre O of the disc and perpendicular to the plane of the disc is :

(A) 8 mR2 (B) 4 mR2

(C)9

40mR2 (D)

9

37mR2

7. A particle moves in circular path with decreasing speed. Which of the following is correct

(A) L

is constant

(B) only direction of L

is constant

(C) acceleration a

is towards the centre

(D) it will move in a spiral and finally reach the centre

8. A solid sphere of radius R has moment of inertia about itsgeometrical axis. If it is melted into a disc of radius r and thickness

t. If it's moment of inertia about the tangential axis (which isperpendicular to plane of the disc), is also equal to , then the valueof r is equal to :

(A)15

2R (B)

5

2R

(C)15

3R (D)

15

3R

PC

Q

a

F

2a

2a

Physics

8/12/2019 Exam_Paper_22.12.2013


Response at www.iitjeeguru.inA-49, Maulana Azad Sarani, City Centre, Durgapur-16, (WB) Call-7699999929


9. One quarter sector is cut from a uniform circular disc of radius R. This sector

has mass M . It is made to rotate about a line perpendicular to its plane andpassing through the centre of the original disc. Its moment of inertial about the

axis of rotation is :

(A)2

1MR2 (B)

4

1MR2 (C)

8

1MR2 (D) 2 MR2

10. A cubical block of side a is moving with velocity v on a horizontal smooth

plane, as shown It hits a ridge at point O. The angular speed of the block

after it hits O is .

(A)a4

v3(B)

a2

v3(C)

a2

v3(D) zero

11. A cubical block of side L rests on a rough horizontal surface withcoefficient of friction . A horizontal force F is applied on the block asshown If the coefficient of frict ion is sufficiently high so that the block

does not slide before toppling, the minimum force required to topple theblock is L F (toppling) -

(A) Infinitesimal (B)4

mg(C) mg/2 (D) mg

(1 )

12. A thin wire of length L and uniform density is bent into a circular loopwith centre at O as shown. The moment of inertia of the loop about the

axis XX is

(A)

L3

28(B)

L3

216(C)

5

16

3

2

L

(D)3

8

3

2

L

13. An equi lateral t riangle ABC formed from a uniform wire has two smallidentical beads initially located at A. The triangle is set rotating about the

vertical axis AO. Then the beads are released from rest simultaneouslyand allowed to sl ide down, one along AB and the other along AC as shown.

Neglecting frictional effects, the quantities that are conserved as the beadsslide down, are

(A) Angular velocity and total energy (kinetic energy and potential energy)(B) Total angular momentum and total energy

(C) Angular velocity and moment of inertia about the axis of rotation(D) Total angular momentum and moment of inertia about the axis of rotation

14. A smooth sphere 'A' is mov ing on a frictionless horizontal plane with angular speed and centreof mass velocity 'v '. It collides elastically and head on with an identical sphere 'B' at rest. Neglect

friction everywhere. After the collision, their angular speeds are Aand

B, respectively. Then

(A) A< B (B) A = B (C) A= (D) B=

15. A disc of mass M and radius R is rolling with angular speed on a horizontalplane as shown. The magnitude of angular momentum of the disc aboutthe origin O is

(A) (1/2)MR2 (B) MR2 (C) (3/2)MR2 (D) 2MR2

8/12/2019 Exam_Paper_22.12.2013



16. Let be the moment of inertia of a uniform square plate about an axis ABthat passes through its centre and is parallel to two of its sides. CD is aline in the plane of the plate that passes through the centre of the plateand makes an angle with AB. The moment of inertia of the plate aboutthe axis CD is then equal to

(A) I (B) I sin2 (C) I cos2 (D) I cos2(/2)

17. A mass m is mov ing with a constant veloci ty along a line parallel to the, x-axis, away from the

origin. Its angular momentum with respect to the origin :

(A) Is zero (B) Remains constant

(C) Goes on increasing (D) Goes on decreasing

18. A hollow smooth uniform sphere A of mass m rolls without sliding on a smooth horizontal surface. Itcollides elastically and headon with another stationary smooth solid sphere B of the same mass m

and same radius. The ratio of kinetic energy of B to that of A just after the collision is :

(A) 5 : 2 (B) 1 : 1 (C) 2 : 3 (D) 3 : 2

19. As shown in the f igure, a disc of mass m is rol ling without sl ipping

a angular velocity . When it crosses point B disc will be in :(A) translational motion only (B) pure rolling motion

(C) rotational motion only (D) none of these

20. A disc of radius R rol ls on a rough horizontal surface. The linear distancecovered by the point A in one complete revolution is:

(A) 8 R (B) 4 3 R (C) 2 3 R (D) none of these

21. A large spool of rope lies on the ground as shown in the fig. Theend, labelled X is pulled a distance S in the horizontal direct ion.

The spool rolls without slipping. The centre of mass of the spoolmoves a distance

(A) 2S (B) S (C) S/2 (D) S/4

22. In the pulley system shown, if radii of the bigger and smaller

pulley are 2m and 1

m respectively and the acceleration of block

A is 5 m/s

2

in the downward direction, then the acceleration ofblock B will be:

(A) 0 m/s2 (B) 5 m/s2 (C) 10 m/s2 (D*) 5/2 m/s2

23. A uniform rod of length is placed symmetrically on two walls as

shown in figure. The rod is in equilibrium. If N1and N2are thenormal forces exerted by the walls on the rod then

(A) N1> N2 (B) N1> N2(C) N1= N2(D) N1and N2would be in the vertical directions. N1 N2

8/12/2019 Exam_Paper_22.12.2013




24. Four forces tangent to the circle of radius R are acting on a

wheel as shown in the figure. The resultant equivalent one forcesystem will be :

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

25. A square plate of edge a/2 is cut out from a uniform square

plate of edge 'a' as shown in figure. The mass of theremaining portion is M. The moment of inertia of the

shaded portion about an axis passing through 'O' (centreof the square of side a) and perpendicular to plane of theplate is :

(A)64

9Ma2 (B)

16

3Ma2

(C)12

5Ma2 (D)

6

Ma2

26. Moment of inertia of a disc about OOis:

(A)3

2

2m r(B)

m r2

2

(C)5

2

2m r(D)

5

4

2m r

O O

m

r

27. A uniform rectangular plate of mass m which is f ree to rotate

about the smooth vertical hinge passing through the centre andperpendicular to the plate, is lying on a smooth horizontal surface.

A particle of mass m moving with speed 'u' coll ides with the plateand sticks to it as shown in figure. The angular velocity of the

plate after collision will be :

(A)a

u

5

12(B)

a

u

19

12(C)

a

u

2

3(D)

a

u

5

3

28. A body of mass m and radius r is rotated with angular veloci ty

as shown in the figure & kept on a surface that has sufficientfriction then the body will move :

(A) backward first and then move forward

(B) forward first and then move backward(C) will always move forward(D) none of these

8/12/2019 Exam_Paper_22.12.2013



29. A sphere of mass 'm

' is given some angular velocity about a

horizontal axis through its centre and gently placed on a plank of

mass 'm

'. The co-efficient of friction between the two is . The

plank rests on a smooth horizontal surface. The initial acceleration

of the centre of sphere relative to the plank will be :

(A) zero (B) g (C) (7/5) g (D) 2 g

30. A small block of mass m is rigidly attached at P to a ring of mass 3m

and radius r. The system is released from rest at = 90 and rollswithout sliding. The angular acceleration of ring just after release is

(A)r4

g(B)

r8

g(C)

r3

g(D)

r2

g

31. An ellipse and a hyperbola have the same centre origin, the same foci and the minor-axis of the

one is the same as the conjugate axis of the other. If e 1, e2be their eccentricities respectively,

then1 1

12

22e e

=

(A) 1 (B) 2 (C) 4 (D) none

32. The line 5x + 12y = 9 touches the hyperbola x 2 9y2= 9 at the point

(A) ( 5, 4/3) (B) (5, 4/3) (C) (3, 1/2) (D) none of these

33. If the foci of the ellipse x yb

2 2

225 = 1 & the hyperbola x y2 2

144 81= 125

coincide then the value of b2

is :

(A) 4 (B) 9 (C) 16 (D) none

34. If hyperbola2

2

b

x

2

2

a

y= 1 passes through the focus of ellipsese

2

2

a

x+

2

2

b

y= 1 then eccentricity of

hyperbola is

(A) 2 (B) 3

2(C) 3 (D) None of these

35. Two conics 2

2

a

x 2

2

b

y=1 and x2=

b

1y intersect if

(A) 0 < b 2

1(B) 0 < a

2

1(C) a2< b2 (D) a2> b2

Mathematics

8/12/2019 Exam_Paper_22.12.2013




36. If both roots of the quadratic equation x2+ x + p = 0 exceed p where p R then p must lie inthe interval:

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

37. If , & are the roots of the equation, x3x 1 = 0 then,

1

1+

1

1+

1

1has the value

equal to:

(A) zero (B) 1 (C) 7 (D) 1

38. If the distance between the focii of an ellipse is equal to the length of its latus rectum, the

eccentricity of the ellipse is :

(A)2

15(B)

2

15(C)

2

25(D)

3

2

39. An ellipse has OB as semi-minor axis, F and Fits foci and the angle FBF is a right angle. Then, theeccentricity of the ellipse is

(A)4

1(B)

3

1(C)

2

1(D)

2

1

40. The angle between the tangents drawn from the point (1, 4) to the parabola y 2= 4x is

(A)2

(B)

3

(C)

4

(D)

6

41. Let P be the point (1, 0) and Q a point of the locus y2= 8x. The locus of mid point of PQ is

(A) x2+ 4y + 2 = 0 (B) x2 4y + 2 = 0 (C) y2 4x + 2 = 0 (D) y2+ 4x + 2 = 0

42. The set of values of 'b' for which the origin and the point (1, 1) lie on the same side of the

straight line, a2x + aby + 1 = 0 a R, b > 0 are :

(A) b (2, 4) (B) b (0, 2) (C) b [0, 2] (D) (2, )\

43. The lines ax + by + c = 0, where 3a + 2b + 4c = 0 are concurrent at the point :

(A)

4

3,

2

1(B) (1, 3) (C) (3, 1) (D)

2

1,

4

3

44. Drawn from the origin are two mutually perpendicular straight lines forming an isosceles trian

gle together with the straight line, 2x + y = a. Then the area of the triangle is :

(A)a 2

2(B)

a 2

3(C)

a 2

5(D) none

45. IfBsinAsin =

23 and

BcosAcos =

25 , 0 < A, B

8/12/2019 Exam_Paper_22.12.2013



47. 290cos1

+ 250sin3

1=

(A)3

32(B)

3

34(C) 3 (D) none

48. nLimit ( ) ! ( ) !

( ) !

n n

n

2 1

3, n N =

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

49. 3xLimit

)92x(

)2x(ln)27x( 3

=

(A) 8 (B) 8 (C) 9 (D) 9

50. 1xLimit

1x

100x100

1k

k

=

(A) 0 (B) 5050 (C) 4550 (D) 5050

51. The value of

0

50

1

50+

1

50

2

50+...........+

49

50

50

50is, where nC

r

=

r

n

(A)

50

100(B)

51

100(C)

25

50(D)

2

25

50

52. (1 + x) (1 + x + x2) (1 + x + x2+ x 3)...... (1 + x + x2+...... + x100) when written in the ascending

power of x then the highest exponent of x is

(A) 505 (B) 5050 (C) 100 (D) 50

53. If

a

1,a ,

b

1,b ,

c

1,c &

d

1,d are four distinct points on a circle of radius 4 units then, abcd

is equal to:(A) 4 (B) 16 (C) 1 (D) none

54. The centre of a ci rcle passing through the points (0, 0), (1, 0) & touching the circle x2+ y2= 9 is:

(A)

2

1,

2

3(B)

2

3,

2

1(C)

2

1,

2

1(D)

2,

2

1

55.

n x

x n x

| |

| |1dx equals :

(A)2

3

1 n x (nx 2) + c (B)2

3

1 n x (nx+ 2) + c

(C)1

31 n x (nx 2) + c (D) 2 1 n x (3 nx 2) + c

56. )]x(g)x(f)x(g)x(f[ dx is equal to

(A))x(g

)x(f

(B) f(x) g(x) f(x) g(x)

(C) f(x) g(x) f(x) g(x) (D) f(x) g(x) + f(x) g(x)

8/12/2019 Exam_Paper_22.12.2013




57. If a1, a

2,... a

nare in A.P. with common difference d 0, then the sum of the series

(sin d) [cosec a1cosec a

2+ cosec a

2cosec a

3+ ... + cosec a

n1cosec a

n]

(A) sec a1 sec a

n(B) cosec a

1 cosec a

n

(C) cot a1 cot a

n(D) tan a

1 tan a

n

58. The sum of the series4log

1

2+

4log

1

4+

4log

1

8+ ...... + 4log

1

n2is

(A) 2

1

n (n + 1) (B) 12

1

n (n + 1) (2n + 1)

(C))1n(n

1

(D) 41

n (n + 1)

59. Let z1, z2, z3be three distinct complex numbers satisfying z1- 1 = z2- 1 = z3- 1.

If z1+ z

2+ z

3= 3 then z

1, z

2, z

3must represent the vertices of :

(A) an equilateral triangle (B) an isosceles triangle which is not equilateral

(C) a right triangle (D) nothing definite can be said

60.

1 1 1 ....... is equal to :

(A) w or w2 (B) - w or - w2 (C) 1 + i or 1 - i (D) - 1 + i or - 1 - i

where w is the imaginary cube root of unity and i = 1

SPACE FOR ROUGH WORK

8/12/2019 Exam_Paper_22.12.2013



62. The reaction CH4(g) + Cl2(g) CH3Cl(g) + HCl(g) has DH = 25 kCal.

From the given data, what is the bond energy of ClCl bond(A) 70 kCal (B) 80 kCal (C) 67.75 kCal (D) 57.75 kCal

63. If x1, x2and x3are enthalpies of HH, O=O and OH bonds respectively, and x4is the enthalpy

of vaporisation of water, estimate the standard enthalpy of combustion of hydrogen

(A) x1+

2

x22x

3+x

4(B) x

1+

2

x22x

3x

4(C) x

1+

2

x2x

3+x

4(D) 2x

3x

1

2

x2x

4

64. DrH of which of the following reactions is zero?

(A) H2(g) 2H+(g) + 2e (B) 2H(g) + aq 2H+(aq) + 2e

(C) 2H(g) 2H+(g) + 2e (D) H2(g) + aq 2H+(aq) + 2e

65. Ethanol can undergoes decomposition to form two sets of products

C2H5OH (g)

if the molar ratio of C2H

4to CH

3CHO is 8 : 1 in a set of product gases, then the energy

involved in the decomposition of 1 mole of ethanolis

(A) 65.98 kJ (B) 48.137 kJ (C) 48.46 kJ (D) 57.22 kJ

61. From the following data at 25C

Reaction DrH kJ/mol

2

1H2(g) + 2

1O2(g) OH (g) 42

H2(g) + 2

1O2(g) H2O(g) 242

H2(g) 2H(g) 436O2(g) 2O(g) 495

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

Statement (a) : DrH for the reaction H

2O (g) 2H(g) + O(g) is 925.5 kJ/mol

Statement (b) : DrH for the reaction OH(g) H(g) + O(g) is 502 kJ/mol

Statement (c) : Enthalpy of formation of H(g) is 218 kJ/mol

Statement (d) : Enthalpy of formation of OH(g) is 42 kJ/mol

(A) Statement c (B) Statement a, b, d (C) Statement b, c (D) Statement a, d

Chemistry

Bond

Bond

Energy

kCal

CCl 84HCl 103CH xClCl y

x : y = 9 : 5

8/12/2019 Exam_Paper_22.12.2013




67. The bond order of nitric oxide is

(A)1

22

(B) 2

(C) 3 (D)1

12

68. Hydrogen fluoride is a liquid unlike other hydrogen halides because

(A) HF molecules combine by hydrogen bonding

(B) F2is highly reactive

(C) F atom has a high electron affinity

(D) HF is a weak acid

69. A NH3molecule attaches itself to a hydrogen ion leading to the formation of NH4+by

(A) an electrovalent bond (B) a coordinate bond

(C) a covalent bond (D) a hydrogen bond

70. A molecule will be stable if the value of bond order is

(A) zero (B) positive(C) negative (D) bond order has no correlation with stability

71. Which of the following does not show resonance?

(A) NO3 (B) C6H6

(C) CO32 (D) SiO

2

72. Which of the following has the smallest bond length?

(A) O2 (B) N2(C) Cl

2(D) HCl

73. Which of the following bonds can be dissociated most easily?

(A) OO (B) CC

(C) NN (D) HH

74. Two atoms X and Y have an electronegativity difference equal to 2.0. What will be the percentage of

covalent character in the molecule?

(A) 46% (B) 54%

(C) 72% (D) 23%

75. The dipole moment of a XY molecule is 1.03 D. If the XY bond distance is 1.26A, what is the

percentage of ionic character in the XY bond?

(A) 39% (B) 60%

(C) 17% (D) 29%

76. In which of the following molecules resonance is equivalent :

(A) HCOOQ (B) CH2= CH CH = CH

2

(C) (D)

66.0fH of water is 285.8 kJ mol

1. If enthalpy of neutralisation of monoacid strong base is

57.3 kJ mol1,0fH of OH

ion will be

(A) 228.5 kJ mol1 (B) 228.5 kJ mol1 (C) 114.25 kJ mol1(D) 114.25 kJ mol1

8/12/2019 Exam_Paper_22.12.2013



77. CH3O CH = CH NO

2I

CH2= CH NO2 II

CH2= CH Cl III

CH2= CH2 IV

Which of the following is the correct order of C C bond lengths among these compounds :

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

78. Which of the following has longest C O bond :

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

79. The IUPAC name of CH2CHC(CH3)2

OH

CH(CH3)2

is

(A) 1-phenyl-3, 4, dimethyl butanol (B) 4-phenyl-3-di-2-methyl butanol

(C) 3-benzyl-2, 4-dimethyl -2-pentanol (D) 4-benzyl-3di-2 methyl-2-butanol

80. Which of the following compounds can exhibit tautoimerism :

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

81. In a compound

C = C

the number of sigma and pi bonds respectively are

(A) 19, 11 (B) 19, 5 (C) 13, 11 (D) 7, 3

82. Which of the following arrangements of electrons in mostly likely to be stable:

(A) (B)

(C) (D)

83. The electrons, identified by quantum by numbers n and l , (i) 1,4 ln (ii) 0,4 ln

(iii) 2,3 ln (iv) 1,3 ln can be placed in order of increasing energy, from the lowest to highest,as

(A) (iv) < (ii) < (iii) < (i) (B) (ii) < (iv) < (i) < (iii)(C) (i) < (iii) < (ii) < (iv) (D) (iii) < (i) < (iv) < (ii)

84. Which electron level would allow the hydrogen atom to absorb a photon but not emit a photon

(A) 3s (B) 2p (C) 2s (D*) 1s

8/12/2019 Exam_Paper_22.12.2013




85.

Hydrogenation of the above compound in the presence of poisoned paladium catalyst gives

(A) An optically active compound (B) An optically inactive compound

(C) A racemic mixture (D) A diastereomeric mixture

86. Consider the following reactions

3

33

CHD||

CHCHCHCH + X + HBr

Identify the structure of the major product X

(A)

3

2

3

CHD||

HCCHCHCH (B)

3

3

3

CHD||

CHCCHCH

(C)

3

3

3

CHD||

CHCHCCH (D)

2

3

3

CH|

CHCHHCCH

87. Which one of the following alkenes will react fastest with H2under catalytic hydrogenation condition

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

88. According to Graham's law , at a given temperature the ratio of the rates of diffusionB

A

r

rof gases AA

and B is given by :

(A)B

A

P

P

2/1

B

A

M

M

(B)

B

A

M

M

2/1

B

A

P

P

(C)

B

A

P

P

2/1

A

B

M

M

(D)

B

A

M

M

2/1

A

B

P

P

89. Which one of the following V, T plots represents the behaviour of one mole of an ideal gas at one

atmp?

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

8/12/2019 Exam_Paper_22.12.2013

13/13

90.

where Z =nRT

PV,

a = Van der Waal's constant for pressure correction

b = Van der Waal's constant for volume correction

Pick the only incorrect statement

(A) for gas A, if a = 0, the compressibility factor is directly proportional to pressure

(B) for gas B, if b = 0, the compressibility factor is directly proportional to pressure

(C) for gas C, a 0, b 0, it can be used to calculate a and b by giving lowest P value and its

intercept with Z = 1.

(D) slope for all three gases at high pressure (not shown in graph) is positive.

SPACE FOR ROUGH WORK

exam_paper_22.12.2013

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