PHYSICS 1. A solid iron sphere A rolls down an inclined plane, while

another hollow sphere B with the same mass and same radius also rolls down the inclined plane. If VA and VB are their velocities at the bottom of the inclined plane, then (A) VA > VB (B) VA = VB (C) VA < VB (D) VA > = < VB

2. A uniform disc of mass m and radius R is rolling on a rough

inclined plane which makes an angle 30° with the horizontal. If the coefficient of static and kinetic friction are each to and

the only forces acting are gravitational and frictional, then what will be the magnitude of the frictional force acting on the disc?

(A) Mg

2 (B)

Mg

4

(C) Mg

6 (D) Mg

3. Consider a uniform bar for which the centre of gravity

coincides with the geometrical centre. Weight of rod and length are W and L respectively. Mark the INCORRECT statement about the rod.

(A) Total gravitational torque about P may be considered as arising from a single force w at the bar's centre.

(B) Total gravitational torque about P may be considered as

arising from a two individual forces of magnitudes wx

L and

w(L x)

L acting at the midpoints of the two segments

defined by P. (C) If a fulcrum is placed at P the rod is balanced if x = L/2 (D) Total gravitational torque about P may be considered as

arising from a two individual forces of magnitudes wx

L and

w(L x)

L acting at the midpoints of the two segments

defined by P.

4. When the electrical conductivity of a semi- conductor is due to the breaking of its covalent bonds, then the semiconductor is said to be

(A) Donar (B) Acceptor (C) Intrinsic (D) Extrinsic

5. On the bombardment of neutron with Boron 10

5B . -particle is

emitted and product nuclei formed is

(A) 126C (B) 6

3Li

P

L

x

(C) 73Li (D) 9

4Be

6. Energy levels A, B, C of a certain atom corresponding to

increasing values of energy i.e. A B CE E E . If 1 2 3, , are

the wavelengths of radiations corresponding to the transitions C to B, B to A and C to A respectively, which of the following statements is correct

(A) 3 1 2 (B)

1 23

1 2

(C) 1 2 3 0 (D) 2 2 23 1 2

7. In an X-rays tube, the intensity of the emitted X-rays beam is

increased by (A) Increasing the filament current (B) Decreasing the filament current (C) Increasing the target potential (D) Decreasing the target potential 8. An electron of mass m when accelerated through a potential

difference V has de-Broglie wavelength . The de-Broglie

wavelength associated with a proton of mass M accelerated through the same potential difference will be

(A) m

M (B)

m

M

(C) M

m (D)

M

m

9. An alternating voltage E 200 2 sin(100t) is connected to a 1

microfarad capacitor through an ac ammeter. The reading of the ammeter shall be (A) 10 mA (B) 20 mA (C) 40 mA (D) 80 mA

10. A metallic ring connected to a rod oscillates freely like a

pendulum. If now a magnetic field is applied in horizontal direction so that the pendulum now swings through the field, the pendulum will

(A) Keep oscillating with the old time period (B) Keep oscillating with a smaller time period (C) Keep oscillating with a larger time period (D) Come to rest very soon

11. A thin circular loop carrying a current has a magnetic moment M. The shape of the loop is changed to a square and it carries the same current. It will have a magnetic moment

(A) M (B) 2

4M

(C)

4M (D)

M

4

12. Which of the following statement is true

(A) The presence of a large magnetic flux through a coil maintains a current in the coil if the circuit is continuous

(B) A coil of a metal wire kept stationary in a non-uniform magnetic field has an e.m.f. induced in it

(C) A charged particle enters a region of uniform magnetic field at an angle of 85° to the magnetic lines of force; the path of the particle is a circle

(D) There is no change in the energy of a charged particle moving in a magnetic field although a magnetic force is acting on it

13. A thin lens made of glass of refractive index 1.5 has a front

surface + 11 D power and back surface – 6 D. If this lens is submerged in a liquid of refractive index 1.6, the resulting power of the lens is

(A) – 0.5 D (B) + 0.5 D (C) – 0.625 D (D) + 0.625 D

14. In a Young’s double slit experiment, 12 fringes are observed to

be formed in a certain segment of the screen when light of wavelength 600 nm is used. If the wavelength of light is changed to 400 nm, number of fringes observed in the same segment of the screen is given by (A) 12 (B) 18 (C) 24 (D) 30

15. For measurement of potential difference, potentiometer is

preferred in comparison to voltmeter because (A) Potentiometer is more sensitive than voltmeter (B) The resistance of potentiometer is less than voltmeter (C) Potentiometer is cheaper than voltmeter (D) Potentiometer does not take current from the circuit 16. The reading of the ammeter in following circuit is

(A) 1

A8

(B) 3

A4

(C) 1

A2

(D) 2 A

17. A cylinder of radius R and length L is placed in a uniform

electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by

(A) 22 R E (B) 2R E

(C) 2(2 R 2 R )E (D) Zero

18. The distance between the plates of a parallel plate condenser

is 8mm and P.D. 120 volts . If a 6mm thick slab of dielectric

constant 6 is introduced between its plates, then (A) The charge on the condenser will be doubled (B) The charge on the condenser will be reduced to half (C) The P.D. across the condenser will be 320 volts

(D) The P.D. across the condenser will be 45 volts

19. Two equal negative charge – q are fixed at the fixed points

(0,a) and (0, a) on the Y-axis. A positive charge Q is

released from rest at the point (2a,0) on the X-axis. The

charge Q will (A) Execute simple harmonic motion about the origin (B) Move to the origin and remain at rest (C) Move to infinity (D) Execute oscillatory but not simple harmonic motion

20. If radius of the sphere is (5.3 0.1) cm. Then percentage error

in its volume will be

(A) 100

3 6.015.3

(B) 1 100

0.013 5.3

(C)

3 0.1100

5.3 (D)

0.1100

5.3

21. A dimensionally consistent relation for the volume V of a

liquid of coefficient of viscosity flowing per second through a

tube of radius r and length and having a pressure difference p across its end, is

(A)

4prV

8 (B)

4V

8pr

(C)

4

8pV

r (D)

4

pV

8 r

22. The wavelength of maximum intensity of radiation emitted by a star is 289.8 nm. The radiation intensity for the

star is: (Stefan’s constant 8 2 45.67 10 Wm K , constant

b 2898 mK) -

(A) 8 25.67 10 W/m (B) 12 25.67 10 W/m

(C) 7 210.67 10 W/m (D) 14 210.67 10 W/m

23. The P-V diagram of 2 gm of helium gas for a certain process A B is shown in the figure. what is the heat given to the gas

during the process A B

(A) o o4P V (B) o o6P V

(C) o o4.5P V (D) o o2P V

24. Pressure versus temperature graphs of an ideal gas are as

shown in figure. Choose the INCORRECT statement

(A) Density of gas is increasing in graph (i) (B) Density of gas is decreasing in graph (ii) (C) Density of gas is constant in graph (iii) (D) None of these

25. Two trains, one coming towards and another going away from an observer both at 4 m/s produce whistle simultaneously of frequency 300 Hz. Find the number of beats produced (A) 5 (B) 6 (C) 7 (D) 12

26. When a wave travels in a medium, the particle displacement is

given by y(x,t) 0.03sin (2t 0.01x) where y and x are

meters and t in seconds. The phase difference, at a given instant of time between two particle 25 m. apart in the medium, is

(A)

8 (B)

4

(C)

2 (D)

27. Time period of a block suspended from the upper plate of a parallel plate capacitor by a spring of stiffness k is T. When block is uncharged. If a charge q is given to the block them, the new time period of oscillation will be

(A) T (B) T (C) T (D) T 28. A cubical block of wood 10 cm on a side floats at the interface

between oil and water with its lower surface horizontal and 4 cm below the interface. The density of oil is 0.6 gcm–3. The mass of block is

(A) 706 g (B) 607 g (C) 760 g (D) 670 g

29. If the work done in blowing a bubble of volume V is W, then

the work done in blowing the bubble of volume 2V from the same soap solution will be

(A) W/2 (B) 2 W

(C) 3 2 W (D) 3 4 W

30. The speed of a body moving with uniform acceleration is u.

This speed is doubled while covering a distance S. When it covers an additional distance S, its speed would become

(A) 3 u (B) 5 u

(C) 11u (D) 7 u

2NH

2NH

2NH

CHEMISTRY 31. The edge length of face centred unit cubic cell is 508pm. If the

radius of the cation is 110 pm. The radius of the anion is: (A) 285pm (B) 398pm (C)144pm (D) 618pm

32. 2 2 2 4

2 8 3

KNH H Br /CCl

Cl (CH ) Cl Pd CaCOHC CH A B C

2 3KNH Na, NH (l)

2moleD E,E is

(A) (B)

(C) (D) None of these

33. In the redox reaction ;

4 3 3 2 2xKMnO yNH KNO MnO KOH H O

(A) x 4, y 6 (B) x 3, y 8

(C) x 8, y 6 (D) x 8, y 3

34. For gaseous state, if most probable speed is denoted by *

'C

average speed by C and mean square speed by C, then for

large no. of molecules the ratio of these speeds are: (A) 1:1.128:1.225 (B) 1:1.225: 1.128 (C) 1.225:1.128:1 (D) 1.128: 1.225:1

35. Consider the following three amines: (I) (II)

(III)

Arrange C N bond length of these compounds in

decreasing order (A) I>II>III (B) I>III>II (C) III>II>I (D) II>III>I

BrBr

Br

Br

OHBr

OH

Br

36. The reaction of HBr with following compound would be:

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

37. The IUPAC name for 2 2 2 2 3K [Cr(CN) O (O )NH ] is:

(A) Potassium amminedicyanotetraoxo chromium(III) (B) Potassium amminedicyanodioxygendioxo chromate(IV) (C) Potassium amminedicyanosuperoxoperoxo chromate(III) (D) Potassium amminedicyanodioxoperoxo chromate(VI)

38. Potassium permanganate acts an oxidant in neutral, alkaline as well as acidic media. The final products obtained from it in the three conditions are respectively.

(A) 2

2 2MnO ,MnO ,Mn

(B) 2 3 2

4MnO ,Mn ,Mn

(C) 2 3

2 4MnO ,MnO ,Mn

(D) 2

4MnO,MnO ,Mn

39. 60 gm of oleum (labelled as 118%) is mixed with 11.8gm water

what will be the composition of final mixture:

(A) Only 2 4H SO having mass 71.8 gm

(B) 118 gm of 2 4H SO

(C) 70.8 gm 2 4H SO and 1 gm water

(D) 32 gm 3SO and 39.8 gm 2 4H SO

40. Uncertanity in position is twice the uncertainty in momentum

uncertainty in velocity is:

(A) h

(B)

1 h

2m

(C) 1

h2m

(D) h

4

OH

41. What is value of Kp of for the following reaction:

2 2 2 4N (g) 2O (g) N O (g)

2 4 2

1N O (g) NO (g)

2

pK x ….(i)

2 2 2 p

1N (g) O (g) NO (g) K y

2 …..(ii)

(A) y

x (B)

2

2

y

x

(C)

2

2

x

y (D)

2xy

42. n moles of helium gas are placed in a vessel of volume V litre

at TK. If V is free volume of helium, then diameter of He

atom is:

(A)

1/3

e

A

V3

2 N .n

(B)

1/3

e

A

3(V V )

2 N .n

(C)

1/3

e

A

6(V V ()

N .n

(D)

1/3

e

A

6V

.N .n

43. The boiling point of an aqueous solution of a non-volatile

solute is 100.o15 C . What is the freezing point of an aqueous

solution obtained by diluting above solution with an equal volume of water.

1 1

f b(K 1.86molality , K 0.512molality )

(A) o0.544 C (B)

o0.52 C

(C) o0.272 C (D)

o1.86 C

44. For the reaction A 2B Products (started with

concentration taken in stochiometric proportion) The experimental determined rate law is:

dAK [A]. [B]

dt

The half time of the reaction would be:

(A) 0.693

K (B)

0.693

1/ K

(C) 0.693

2K (D) Not defined

0.54V 0.45V 1.07V3 2

1ClO ClO Cl Cl

2

0.76V

oE

R R

Si O Si

O O

Si O Si

45. At o0 C , ice and water are in equilibrium. The value of G

and S for the conversion of ice to liquid water are o

fusion for ice( H 6000J/mol)

(A) 0 and 21.98 1 1JK mol

(B) ve and zero

(C) 1 1ve and 21.98JK mol

(D) Zero and zero

46.

The oE in the given figure is:

(A) 0.5 (B) 0.6 (C) 0.7 (D) 0.8

47. The correct order of hybridization of central atom in the

following species 2

3 4 5 3NH [PtCl ] ,PCl andBCl is:

(A) 2 3 2 3dsp ,dsp ,sp ,sp

(B) 3 2 3 2sp ,dsp ,sp d,sp

(C) 3 2 3 3sp ,sp ,sp ,dsp

(D) 2 3 2 3dsp ,sp ,sp ,dsp

48. In orthorhombic the value of a, b and c are respectively:

..4.2A , 8.6A and 8.3

.A , given the molecular mass of the

solute is 155 g1mol and that

of density is 3.3 g/cc. The

number of formula unit per unit cell is: (A) 2 (B) 3 (C) 4 (D) 6

49. On addition of 1 ml solution of 10% NaCl to 10 ml gold sol in the presence of 0.25 gm of starch, the coagulation just prevented, starch has the following gold no.: (A) 0.025 (B) 0.25 (C) 0.5 (D) 250

50. On controlled hydrolysis and condensation 3R SiCl yields:

(A) 3 3R Si O SiR (B) 3 3 n( R Si O SiR )

(C) 3R SiOH (D)

51. Iron pipes-lying under acidic soil are often attached to blocks of magnesium fro protection from rusting magnesium offers protection of iron against corrosion because it: (A) More readily converted into positive ion (B) Is lighter than iron (C) Form a corrosion resistant alloy with iron (D) Prevents air from reaching surface of iron.

52. A white solid ‘A’ on heating gives off gas which turns lime water milky. The residue is yellow when hot but turns white on cooling. The solid ‘A’ is:

(A) 4ZnSO (B) 3ZnCO

(C) 4PbSO (D) 3PbCO

53. Tautomerism is exhibited by:

(A) 3 3(CH ) CNO (B) 3 2(CH ) NH

(C) 3 2R CNO (D) 2 2RCH NO

54. The compound X on reaction with 4 2 4HgSO H SO gives y

which on oxidation gives acetic acid X is:

(A) 2 2C H (B) 2 4C H

(C) 3 4C H (D) 4 6C H

55. Replacement of Cl of chlorobenzene to give phenol requires-

drastic condition but chlorine of 2,4-dinitrochlorobenzene is readily replaced because:

(A) 2NO make ring electron rich at ortho and para

(B) 2NO withdraw e from meta position

(C) 2NO donate e at meta position

(D) 2NO withdraw e from ortho/para position

56. An organic compound X is oxidized by using acidified

2 2 7K Cr O . The product obtained reacts with phenyl hydrazine

but does not give silver mirror test. The possible structures is:

(A) 3 3CH COCH (B) 3 2(CH ) CHOH

(C) 3CH CHO (D) 3 2CH CH OH

57. An organic compound ‘A’ has molecular formula 3 6C H O . It

undergoes iodoform test. When saturated with dil. HCl it give

‘B’ of molecular formula 9 4C H O . A & B respectively are:

(A) Propanal and mesitylene (B) Propanone and mesitylene (C) Propanone and 2,6-dimethyl-2,5-heptadien-4-one (D) Propanone and mesitylene oxide

1R

2R 3N R

58. 2 2R CH CH OH can be converted into

2 2R CH CH COOH . The correct sequence of the reagent is:

(A)

3 3PBr ,KCN,H O (B) 3 2PBr ,KCN,H

(C)

3HCN.PBr .H (D) KCN,H

59. The compound form nitroso amines. when substituent’s are:

(A) 1 3 2 3R CH , R R H

(B) 1 2 3 2 5R R H, R C H

(C) 1 2 3 3R H, R R CH

(D) 3 2 2 5 3R CH R C H R H

60. Trans form of polyisoprene is:

(A) Gutta percha (B) Hydrochloride rubber (C) Buna-N (D) Synthetic rubber

MATHEMATICS

61. The area of the region bounded by the curves y x 1 and

y 3 x is

(A) 6 sq. unit (B) 2 sq. unit (C) 3 sq. unit (D) 4 sq. unit

62. If y y x & 2 sinx dy

cos xy 1 dx

, y 0 1 then

y2

(A) 1

3 (B)

2

3

(C) 1

3 (D) 1

63. The value of

2x

2

x 1e dx

x 1

is

(A) x x 1e C

x 1

(B) x x 1

e Cx 1

(C) xxe C (D) 2 xx e C

64. The value of

a

2 20

dx

x a x is

(A) 6

(B)

4

(C) 3

(D)

2

65. If 3 a 2C 4 b 3d 0 then the equation

3 2ax bx cx d 0 will have

(A) no real root

(B) at least one real root in 1,0

(C) at least one real root in 0,1

(D) none of these

66. The number of critical points of f x max sinx,cosx for

x 0,2

(A) 2 (B) 5 (C) 3 (D) 4

67. The range of 2f x 2cos x 3cosx 1 is

(A) 0,2 (B) 1,1

2 2

(C) 1

0,2 2

(D) none of these

68.

2/xx x x

x 0

a b clim ,a,b,c 0

3

is equal to

(A) 0 (B) 2/3abc

(C) abc (D) 1/2abc

69. The function 2 2f x x 1 x 3x 2 cos x is not

differentiable at (A) 1 (B) –1 (C) 0 (D) 2

70. For all complex numbers 1 2z ,z satisfying 1z 12 &

2z 3 4i 5 , then minimum and maximum value of

1 2z z is

(A) 0, 12 (B) 2, 22 (C) 2, 12 (D) 7, 22

71. If one root is square of the other root of the equation

2x px q 0 then the relation between p & q is

(A) 3 2p q 3p 1 q 0 (B) 3 2p q 3p 1 q 0

(C) 3 2p q 3p 1 q 0 (D) 3 2p q 3p 1 q 0

72. If x, y, z are real and

2 2 24x 9y 16z 6xy 12yz 8zx 0 then x, y, z are in

(A) AP (B) GP (C) HP (D) none of these

73. If the coefficient of th2r 4 term and thr 2 term in the

expansion of 181 x are equal then r

(A) 5 (B) 6 (C) 7 (D) 8

74. If 25 identical things be distributed among 5 persons then the

number of ways of receiving atleast one things are

(A) 24 4C 5 (B) 24 134 4C 5 C

(C) 24 5C (D) 24 4C

75. Let a die is loaded in such a way that even faces are twice as likely to occur as the odd faces. The probability that a prime number will show up when the die is tossed is

(A) 2

6 (B)

2

9

(C) 4

6 (D)

4

9

76. The probability that a year chosen at random has 53 Sunday is

(A) 1

7 (B)

2

7

(C) 5

28 (D)

3

28

77. If

1 0 0

A 0 1 1

0 2 4

&

1 0 0

I 0 1 0

0 0 1

and

1 21A A cA dI

6

then c&d are

(A) 6, 11 (B) 6, 11 (C) 6,11 (D) 6, 11

78. If , , are the roots of the equation 3 2x x x 1 0 then

2

2

2

1 1 1

1 1 1

1 1 1

(A) 1 (B) 2 (C) 3 (D) 0

79. If a,b,c are unit vectors such that a b c 0 then

a.b b.c c.a

(A) 1 (B) 1

(C) 3

2 (D)

3

2

80. A unit vector / vectors in xy-plane which makes an angle o45

with ˆ ˆi j and an angle o60 with ˆ ˆ3i 4j is

(A) ˆ ˆi & j (B) ˆ ˆ ˆ ˆi j i j

&2 2

(C) ˆ ˆ ˆ ˆi j i j

&2 2

(D) none of these

81. The equation of the plane bisecting the acute angle between

the planes 2x y 2z 3 0 and 3x 2y 6z 8 0 is

(A) 23x 13y 32z 45 0

(B) 23x 13y 32z 45 0

(C) 5x y 4z 45 0

(D) 23x 13y 32z 3 0

82. If the lines x a m, y 2 & y mx are concurrent then

the least value of a is

(A) 0 (B) 2

(C) 2 2 (D) 3 2

83. The equation of a circle which touches the line 2x 3y 1 0

at the point 1, 1 and is orthogonal to the circle having points

0, 1 & 2,3 as the extremities of diameter is

(A) 2 2x y 10x 5y 1 0

(B) 2 22x 2y 10x 5y 1 0

(C) 2 22x 2y 10x 5y 1 0

(D) 2 22x 2y 10x 5y 1 0

84. The radius of the circle touching parabola 2y x at 1,1 and

having directrix as its normal is

(A) 5 5

2 (B)

5 5

4

(C) 5 5

8 (D)

5 5

16

85. Let for all real p, the line 22px y 1 p 1 touches a fixed

ellipse 2 2

2 2

x y1

a b then eccentricity of this ellipse

(A) 1

2 (B)

1

3

(C) 1

2 (D)

3

2

86. The eccentricity of the hyperbola 2 2x 8y 1 0 is

(A) 2 (B) 3

(C) 4 (D) 3

87. If 24sin 2 3 1 cos 4 3 then

(A) 2n3

(B) 2n , 2n

6 3

(C) n4

(D) 2n

4

88. The proposition p ~p ~p p is a

(A) tautology (B) contradiction

(C) neither a tautology nor a contradiction (D) tautology and contradiction

89. are two points on the curve . If P is

a point on the curve at which the tangent to the curve is parallel to the chord AB, then, abscissa of P, is

(A) (B)

(C) (D)

90. If 1 2 3 nx ,x ,x ,...,x are n values of a variable X and

1 2 ny ,y ,...,y are n values of variable Y such that ii

x ay

h

,

i 1,2,....,n then

(A) Var Y Var X (B) 2Var X h Var Y

(C) 2Var Y h Var X (D) 2Var X h Var Y a

A 1,0 ,B e,1 ey log x

e 1

2

e 1

2

e 1 e 1