12

PHYSICS 1. Two particles of equal mass go round a circle of radius R

under the action of their mutual gravitational attraction. The speed of each particle is

(A) 1 1

v2R Gm

(B) Gm

v2R

(C) 1 Gm

v2 R

(D) 4Gm

vR

2. The distance of the centres of moon and earth is D. The mass

of earth is 81 times the mass of the moon. At what distance from the centre of the earth, the gravitational force will be zero

(A) D

2 (B)

2D

3

(C)

4D

3 (D)

9D

10 3. The ratio of the lengths of two wires A and B of same material

is 1 : 2 and the ratio of their diameter is 2 : 1. They are stretched by the same force, then the ratio of increase in length will be

(A) 2 : 1 (B) 1 : 4 (C) 1 : 8 (D) 8 : 1 4. The Young's modulus of a wire of length L and radius r is Y

N/m2. If the length and radius are reduced to L/2 and r/2, then its Young's modulus will be (A) Y/2 (B) Y (C) 2Y (D) 4Y

5. If x longitudinal strain is produced in a wire of Young's

modulus y, then energy stored in the material of the wire per unit volume is

(A) 2yx (B) 22yx

(C) 21y x

2 (D) 21

yx2

6. A siphon in use is demonstrated in the following figure. The

density of the liquid flowing in siphon is 1.5 gm/cc. The pressure difference between the point P and S will be

(A) 105 N/m (B) 2 × 105 N/m (C) Zero (D) Infinity

13

7. Density of ice is and that of water is . What will be the

decrease in volume when a mass M of ice melts

(A)

M (B)

M

(C)

1 1M (D)

1 1 1

M

8. A closed rectangular tank is completely filled with water and is

accelerated horizontally with an acceleration a towards right. Pressure is (i) maximum at, and (ii) minimum at

(A) (i) B (ii) D (B) (i) C (ii) D (C) (i) B (ii) C (D) (i) B (ii) A 9. A vertical U-tube of uniform inner cross section contains

mercury in both sides of its arms. A glycerin (density = 1.3 g/cm3) column of length 10 cm is introduced into one of its arms. Oil of density 0.8 gm/cm3 is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column, Density of mercury = 13.6 g/cm3

(A) 10.4 cm (B) 8.2 cm (C) 7.2 cm (D) 9.6 cm 10. A particle starts S.H.M. from the mean position. Its amplitude

is A and time period is T. At the time when its speed is half of the maximum speed, its displacement y is

(A) A

2 (B)

A

2

(C)

A 3

2 (D)

2A

3

14

11. A 201.00 10 kg particle is vibrating with simple harmonic

motion with a period of 51.00 10 sec and a maximum speed

of 31.00 10 m/s . The maximum displacement of the particle is

(A) 1.59 mm (B) 1.00 m (C) 10 m (D) None of these

12. Which one of the following statements is true for the speed v

and the acceleration a of a particle executing simple harmonic motion (A) When v is maximum, a is maximum (B) Value of a is zero, whatever may be the value of v (C) When v is zero, a is zero (D) When v is maximum, a is zero

13. The angular velocity and the amplitude of a simple pendulum is and a respectively. At a displacement X from the mean

position if its kinetic energy is T and potential energy is V, then the ratio of T to V is

(A) 2 2 2 2 2X / (a X ) (B) 2 2 2X / (a X )

(C) 2 2 2 2 2(a X ) / X (D) 2 2 2(a X ) / X

14. A vertical mass-spring system executes simple harmonic

oscillations with a period of 2 s. A quantity of this system which exhibits simple harmonic variation with a period of 1 s is (A) Velocity

(B) Potential energy (C) Phase difference between acceleration and displacement (D) Difference between kinetic energy and potential energy

15. A pendulum suspended from the ceiling of a train has a period

T, when the train is at rest. When the train is accelerating with a uniform acceleration a, the period of oscillation will

(A) Increase (B) Decrease (C) Remain unaffected (D) Become infinite

16. If the metal bob of a simple pendulum is replaced by a wooden

bob, then its time period will (A) Increase (B) Decrease (C) Remain the same (D) First increase then decrease

15

17. Two bodies M and N of equal masses are suspended from two separate massless springs of force constants k1 and k2 respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude M to that of N is

(A) 1

2

k

k (B) 1

2

k

k

(C) 2

1

k

k (D) 2

1

k

k

18. Five identical springs are used in the following three

configurations. The time periods of vertical oscillations in configurations (i), (ii) and (iii) are in the ratio

(A) 1

1: 2 :2

(B) 1

2 : 2 :2

(C) 1

: 2 :12

(D) 1

2 : :12

19. The motion of a particle varies with time according to the

relation y a(sin t cos t) , then

(A) The motion is oscillatory but not S.H.M. (B) The motion is S.H.M. with amplitude a

(C) The motion is S.H.M. with amplitude a 2

(D) The motion is S.H.M. with amplitude 2a

20. The distance between two consecutive crests in a wave train

produced in a string is 5 cm. If 2 complete waves pass through any point per second, the velocity of the wave is

(A) 10 cm/sec (B) 2.5 cm/sec (C) 5 cm/sec (D) 15 cm/sec 21. A stone is dropped into a lake from a tower 500metre high.

The sound of the splash will be heard by the man approximately after

(A) 11.5 seconds (B) 21 seconds (C) 10 seconds (D) 14 seconds

16

22. Two waves are given by 1y asin( t kx) and

2y acos( t kx) The phase difference between the two

waves is

(A)

4 (B)

(C)

8 (D)

2

23. A plane wave is represented by x 1.2sin(314t 12.56y)

Where x and y are distances measured along in x and y direction in meters and t is time in seconds. This wave has

(A) A wavelength of 0.25 m and travels in + ve x direction (B) A wavelength of 0.25 m and travels in + ve y direction (C) A wavelength of 0.5 m and travels in – ve y direction (D) A wavelength of 0.5 m and travels in – ve x direction 24. When two sound waves with a phase difference of / 2 , and

each having amplitude A and frequency , are superimposed

on each other, then the amplitude and frequency of resultant wave is

(A) A

,22

(B) A

,2

(C)

2 A,2

(D) 2 A,

25. A tuning fork of frequency 100 when sounded together with another tuning fork of unknown frequency produces 2 beats per second. On loading the tuning fork whose frequency is not known and sounded together with a tuning fork of frequency 100 produces one beat, then the frequency of the other tuning fork is (A) 102 (B) 98 (C) 99 (D) 101

26. In a stationary wave, all particles are (A) At rest at the same time twice in every period of oscillation (B) At rest at the same time only once in every period of

oscillation (C) Never at rest at the same time (D) Never at rest at all

27. A wave of frequency 100 Hz is sent along a string towards a fixed end. When this wave travels back after reflection, a node is formed at a distance of 10 cm from the fixed end of the string. The speed of incident (and reflected) wave are

(A) 40 m/s (B) 20 m/s (C) 10 m/s (D) 5 m/s

17

28. In order to double the frequency of the fundamental note

emitted by a stretched string, the length is reduced to 3

4th of

the original length and the tension is changed. The factor by which the tension is to be changed, is

(A) 3

8 (B)

2

3

(C) 8

9 (D)

9

4

29. A cylindrical tube, open at both ends, has a fundamental

frequency 0f in air. The tube is dipped vertically into water

such that half of its length is inside water. The fundamental frequency of the air column now is

(A) 03f / 4 (B) 0f

(C) 0f / 2 (D) 02f

30. An observer is moving towards the stationary source of sound, then

(A) Apparent frequency will be less than the real frequency (B) Apparent frequency will be greater than the real frequency (C) Apparent frequency will be equal to real frequency (D) Only the quality of sound will change

18

CHEMISTRY

31. 4 3 2NH HS(s) NH (g) H S(g)

In the above reaction, if the pressure at equilibrium and at 300

K is 100atm then what will be the equilibrium constant pK ?

(A) 22500 atm (B) 250 atm

(C) 2100 atm (D) 2200 atm

32. 15 moles of 2H and 5.2 moles of 2I are mixed and allowed to

attain equilibrium at o500 C . At equilibrium, the concentration

of HI is found to be 10 moles. The equilibrium constant for the

formation of HI is:

(A) 50 (B) 15

(C) 100 (D) 25

33. For the gaseous reaction,

12 4 2 2 6C H H C H , H 130 kJ mol carried in a

closed vessel, the equilibrium concentration of the 2 6C H can

definitely by increased by:

(A) increasing temperature and decreasing pressure

(B) decreasing temperature and increasing pressure

(C) increasing temperature and pressure both

(D) decreasing temperature and pressure both

34. An acid HA ionizes as, HA H A

The pH of 1.0 M solution is 5. Its dissociation constant would

be:

(A) 191 10 (B) 5

(C) 85 10 (D) 51 10

35. Which statement is false? (Assume complete dissociation in

each case)

(A) If 2.0 L of a solution of 2 4H SO contains 0.1 mole, then pH

of the solution is 2

(B) The concentration of OH in 0.005 M 3HNO is

122.0 10 mol/L

(C) The pH of 0.01 M KOH is 12

(D) In a 0.001 M solution of NaOH the concentration of H is

310 mol/L

19

36. An aqueous solution contains 2 2 2Ni ,Co and Pb ions at

equal concentrations. The solubility product of NiS, PbS and

CoS in water at o25 C and 241.4 10 ,

28 263.4 10 and 3 10 , respectively. Indicate which of

these ions will be precipitate first and last when sulphide

concentration is progressively increased form zero?

(A) NiS and PbS (B) NiS and CoS

(C) CoS and NiS (D) PbS and NiS

37. In which of the following crystals alternate tetrahedral voids

are occupied?

(A) NaCl (B) ZnS

(C) 2CaF (D) 2Na O

38. The packing efficiency of the two dimensional square unit cell

shown below is:

(A) 39.27% (B) 68.02%

(C) 74.05% (D) 78.54%

39. In orthorhombic, the value of a, b and c are respectively 4.2 Å,

8.6 Å and 8.3 Å. Given the molecular mass of the solute is 155

g 1mol and that of density is 3.3 g/cc, the number of formula

units per unit cell is:

(A) 2 (B) 3

(C) 4 (D) 6

40.

The above compound does not contain:

(A) o3 OH group (B) o3 H group

(C) o2 Cl group (D) o3 Br group

l

20

3 2 2

3 3

CH CHCH CH CCH SH| |CH CH

3 2 2 2

32

CH CH CH CH CCH SH|

CHCH

3 2 2CH CHCH CHCH NH|SH

41. The compound 2-Ethylhex-2-ene-1-thiol has the structure:

(A) 2 5 2 2C H CH CHCH CH SH

(B)

(C)

(D)

42. Which of the following functional group is not present in the

given compound:

(A) Amide (B) Carboxylic acid

(C) Ketone (D) Amine

43. are:

(A) Position isomer (B) Metamer

(C) Functional isomer (D) Homologs

44. Resonance is not possible in:

(A) (B)

(C) 2CH CH Cl (D)

45. Which of the following compound is not a resonance

stabilized?

(A) (B)

(C) (D)

21

46. More stable resonating structure of the given cation is:

(A) (B)

(C) (D)

47. Find the total + m groups attached to the benzene ring in the

given compound?

(A) 3 (B) 4

(C) 5 (D) 6

48. Hyperconjugation is not present in:

(A) (B)

(C) (D)

49.

Among threes compounds, the correct order of resonance

energy is:

(A) I>II>III (B) II>I>III

(C) III>I>II (D) I>III>II

22

50. Which N atom can donate its electron pair more easily to

proton?

(A) (B)

(C) (D)

51. Identify the most basic nitrogen atom:

(A) I (B) II

(C) III (D) IV

52. Choose the correct option for acidity order:

(A) (B)

(C) (D)

53. Choose the pair in which second compound is more acidic

than first?

(A) 3 3 3 2CH CH or CH NO (B)

(C) (D)

23

54. Which of the following will not show geometrical isomerism:

(A) (B)

(C) (D)

55. Write correct IUPAC name of following compound:

(A) (1Z, 2Z, 3E) hept-1, 3, 5-triene

(B) (2E, 4Z, 6Z) Hept-2, 4, 6-triene

(C) (3Z, 5E) Hept-1, 3, 5-triene

(D) (2E, 4Z)-Hept-2, 4, 6-triene

56. Which can not show geometrical isomerism?

(A) (B)

(C) (D)

57. Member of which of the following pair of isomers are not

position isomers?

(A)

(B)

(C)

(D)

24

2 2CH C NH

O

2 3CH C OCH

O

2CH C H

O

2 3CH C CH

O

58. are:

(A) Identical compounds (B) Positional isomers

(C) Functional isomers (D) Chain isomers

59. Correct order of stability of carbanion:

(a) (b)

(c) (d)

(A) a>b>c>d (B) b>c>d>a

(C) b>a>c>d (D) a>d>b>c

60.

The products of above reaction will be:

(A) (B)

(C) (D)

25

MATHEMATICS 61. The equation of the straight line upon which the length of the

perpendicular from the origin is 2 and the slope of this

perpendicular is 5

12 can be

(A) 12x 5y 26 0 (B) 5x 12y 26 0

(C) 12x 5y 13 0 (D) 5x 12y 26 0

62. The line joining A 2,0 ,B 3,1 is rotated about A in the

anticlock direction through an angle of o15 . The equation of

the line in the new position is

(A) x 3y 2 0 (B) x 2y 2 0

(C) 3x y 2 3 0 (D) none of these

63. The coordinates of the orthocentre of the triangles bounded by

the lines 4x 7y 10 0,x y 5 and 7x 4y 15 :

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

(C) 1,2 (D) 1, 2

64. Let A 1,1 and AB is any line through it cutting the x-axis in

B. If AC is perpendicular to AB and meet the y-axis in C, then the equation of locus of mid-point P of BC is (A) x y 1 (B) x y 2

(C) x y 2xy (D) 2x 2y 1

65. The angle between the pair of straight lines

2 2 2 2 2x cos 1 xysin y sin 0 is

(A) 3

(B) 4

(C) 2

(D) 6

66. If line passing through point A 0,1 and having slope 2

3

intersect circle 2 2x y 9 at points P and Q, then PA AQ

(A) 8 (B) 6 (C) 4 (D) none of these

67. Two perpendicular chords of equal length having slope

1 2m & m are drawn from origin to the circle

2 2x 1 y 2 5 , then the value of 2 2

1 2m m is equal

to

(A) 80

9 (B)

82

9

(C) 83

9 (D) none of these

26

68. The equation of the smallest circle passing through the

intersection of 2 2x y 2x 4y 4 0 and the line

x y 4 0 is

(A) 2 2x y 3x 5y 8 8 (B) 2 2x y x 3y 0

(C) 2 2x y 3x 5y 0 (D) 2 2x y x 3y 8 0

69. The range of value of for which the point , 1 is exterior

to both the parabola 2y x is

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

(C) 1,0 (D) none of these

70. An equilateral triangle is inscribed in the parabola 2y 4x

one of whose vertex is at the vertex of the parabola, the length of each side of the triangle is

(A) 3

2 (B)

4 3

2

(C) 8 3

2 (D) 8 3

71. The coefficient of 49x in the expansion of x 1

2 49

1 1 1x x .... x

2 2 2 is equal to

(A) 50

12 1

2 (B)

50

12 1

2

(C) 49

12 1

2 (D)

49

12 1

2

72. The term which is independent of „x‟ in the expansion of

181

9x ,3 x

x 0 , is times the corresponding binomial

coefficient. Then „ ‟ is

(A) 3 (B) 1

3

(C) 1

3 (D) 1

73. The expansion of n

1 x has 3 consecutive terms with

coefficients in the ratio 1:2:3 and can be written in the form n n n

k k 1 k 2C : C : C . The sum of all possible values of

n k is

(A) 18 (B) 21 (C) 10 (D) 32

27

74. A committee of 5 is to be chosen from a group of 9 people.

Number of ways in which it can be formed if two particular persons either serve together or not at all and two other particular persons refuse to serve with each other, is (A) 41 (B) 36 (C) 47 (D) 76

75. The number 2006 is made up of exactly two zeros and two other digits whose sum is 8. The number of 4 digit numbers with these properties (including 2006) is (A) 7 (B) 18 (C) 21 (D) 24

76. The letters of word “RADHIKA” are permuted are arranged in alphabetical order as in English dictionary. The number of words appear before the word “RADHIKA” is (A) 2193 (B) 2195 (C) 2119 (D) 2192

77. If a, b, c are distinct positive real in HP, the value of the

expression, b a b c

b a b c is equal to

(A) 1 (B) 2 (C) 3 (D) 4

78. If sum of three numbers in GP is 21 and the sum of their squares is 189, then the common ratio of the GP is

(A) 1

2,2

(B) 1

3,3

(C) 1

4,4

(D) 1

5,5

79. Given & are the roots of the quadratic equation

2x 4x k 0 k 0 . If 3 3, , are in

geometric progression, then the value of „k‟ equals

(A) 4 (B) 16

7

(C) 3

7 (D) 12

80. The sum to infinity of the series 1 1 1

....1 1 2 1 2 3

is

equal to

(A) 2 (B) 5

2

(C) 3 (D) none of these

28

81. If sum of 2 3

7 1 9 1 11 1....

2 3 3 3 4 3 4 5 3 upto 10

terms is equal to

(A) 10

1 1

2 12 3 (B)

10

1 1

3 12 3

(C) 10

1 1

2 10 3 (D) none of these

82. If 1z and 2z are uni-modular complex numbers such that

2 21 2z z 5 , then the value of

221 1 2 2z z z z is equal

to (A) 8 (B) 12 (C) 14 (D) none of these

83. , , are the roots of x3 – 3x2 + 3x + 7 = 0 then

1 1 1

1 1 1

is

(A) 3

(B) 2

(C) 22 (D) 4

84. If z x iy z x iy then the equation 3z i

mz 1

does not

represent a circle when

(A) 1

m2

(B) m =1

(C) m = 2 (D) m = 3

85. If 10 10

z 1 3i 1 3i , then arg z is

(A) 2

(B)

(C) 4

(D) 2

86. If the vertex of parabola is at (2, 0) and the extremities

of the latusrectum are (3, 2) and (3, –2), then the equation of the parabola is

(A) 2y 2x 4 (B) 2x 4y 8

(C) 2y 4x 8 (D) none of these

87. The length of the latusrectum of the conic section

2 2 2169 x 1 y 3 5x 12y 17 is

(A) 14

13 (B)

28

13

(C) 12

13 (D) none of these

29

88. The number of ways to give 16 different things to three

persons A, B, C so that B gets 1 more than A and C gets 2 more than B, is

(A) 16!

4!5!7! (B) 4!5!7!

(C) 16!

3!5!8! (D) 3!5!8!

89. If 0 1 2C ,C ,C ,...., denotes the combinatorial coefficients in the

expansion of 10

1 x , then the value of

20 101 CC CC....

1 2 3 11 is equal to

(A) 1

11 (B)

112 1

11

(C) 0 (D) 113 1

11

90. In how many ways can six boys and five girls stand in a row if

all the boys are to stand together but the girls cannot all stand together? (A) 172,800 (B) 432,000 (C) 345,600 (D) none of these