12

PHYSICS

PARAGRAPH FOR NEXT THREE QUESTIONS: Figure shows a container having ideal liquid of variable density.

The density of liquid varies as

00

3h4

h where h0 is height

of liquid in container, 0 is constant and h is height from bottom. A

solid block of small dimensions of density 05

2 and mass m is

released from bottom of tank. 1. The motion of the block (A) periodic but not SHM

(B) SHM (C) oscillatory but not SHM

(D) oscillatory but not periodic 2. After what time block reaches its initial position?

(A) 05h2

6g (B) 0h

2g

(C) 0h

3g (D) 05h

6g

3. Maximum speed of block is :

(A) 0gh

5 (B) 02gh

(C) 03gh

10 (D) 0

10gh

3

4. The equation of stationary wave along a stretched string is

given by

x

y 5sin cos40 t3

where x and y are in centimetre

and t in second. The separation between two adjacent nodes is : (A) 6 cm (B) 4 cm (C) 3 cm (D) 1.5 cm

5. A steel rod has a radius of 10 mm and a length of 1.0 m. A

force stretches it along its length and produces a strain of

0.16%. Young‟s modulus of the steel is 13 22.0 10 Nm . what

is the magnitude of the force stretching the rod? (A) 100 kN (B) 314 kN (C) 31.4 kN (D) 200 kN 6. The work done per unit volume in deforming a body is given by (A) stress × strain (B) 1/2 (stress × strain) (C) stress/strain (D) strain/stress

13

7. Energy stored in stretching a string per unit volume is

(A) 1

stress strain2

(B) stress strain

(C) 2Y(Strain) (D) 21Y(Stress)

2

8. Minimum and maximum values of Possion‟s ratio for a metal

lies between (A) to (B) 0 to 1

(C) to 1 (D) 0 to 0.5

9. A metallic rod of length l and cross-sectional area A is made of

a material of Young‟s modulus Y. If the rod is elongated by an amount y, then the work done is proportional to

(A) y (B) 1/y (C) y2 (D) 1/y2 10. The frequency of the first harmonic of a string stretched

between two points is 100 Hz. The frequency of the third overtone is

(A) 200 Hz (B) 300 Hz (C) 400 Hz (D) 600 Hz 11. The kinetic energy and the potential energy of a particle

executing S.H.M. are equal. The ratio of its displacement and amplitude will be

(A) 1

2 (B)

3

2

(C) 1

2 (D) 2

12. Equations 1y A sin t and 2A A

y sin t cos t2 2

represent

S.H.M. The ratio of the amplitudes of the two motions is

(A) 1 (B) 2

(C) 0.5 (D) 2

13. The relative velocity of two consecutive layers is 8 cm/s. If the

perpendicular distance between the layers is 0.1 cm, then the velocity gradient will be (A) 8sec–1 (B) 80 sec–1

(C) 0.8 sec–1 (D) 0.08 sec–1

14

14. The equation of SHM of a particle is 2

2

d yky 0,

dt where k is a

positive constant. The time period of motion is given by

(A) 2

k (B)

2

k

(C) 2 k (D) 2 k 15. A pulse on a sting is shown in the figure. P is particle of the

string. Then state which of the following is incorrect.

(A) If P is stationary point, then pulse consists of two waves

travelling in opposite direction (B) If P is moving upwards, then pulse is travelling in positive

direction (C) If P is moving downwards, then pulse is travelling in

negative direction (D) none of these

16. x = x1 + x2 (where x1 = 4 cost and 2x 3 sint) is the

equation of motion of a particle along x-axis. The phase different between x1 and x is

(A) 37° (B) 53° (C) 90° (D) none of these 17. The change in the value of „g‟ at a height „h‟ above the surface

of the earth is the same as at a depth below the surface of earth. When both „d‟ and „h‟ are much smaller than the radius of earth, then, which one of the following is correct?

(A) h

d2

(B) 3h

d2

(C) d 2h (D) d h

18. Find the time period of oscillation

(A) 2

m

k

(B) 2 1

m m

k k

(C) 1 2

m

k k

(D) 2 1 2

m m

k k k

15

19. A transverse wave described by equation y = 0.02 sin (x + 30t) (where x and t are in metres and sec. respectively) is travelling along a wire of area of cross-section 1 mm2 and density 8000 kg/m3. What is the tension in the string?

(A) 20 N (B) 7.2 N (C) 30 N (D) 14.4 N 20. A tunnel is dug along the diameter of the earth (Radius R and

mass M). There is a particle of mass „m‟ at the centre of the tunnel. Find the minimum velocity given to the particle so that it just reaches to the surface of the earth

(A) GM

R

(B)GM

2R

(C) 2GM

R

(D) it will reach with the help of negligible velocity

21. A simple pendulum suspended from the ceiling of a stationary trolley has a length . Its period of oscillation if the trolley moves forward with an acceleration f?

(A)

2f g

(B)

2f g

(C)

1/2

2 22

f g

(D) 2 2

2f g

22. A wire of length l having tension T and radius r vibrates with

fundamental frequency „f‟. Another wire of the same metal with length 2l having tension 2T and radius 2r will vibrate with fundamental frequency

(A) f (B) 2f

(C) f

2 2 (D)

f

2 23. If the ratio of lengths, radii and Young‟s moduli of steel and

brass wires in the figure are a, b and c respectively, then the corresponding ratio of increase in their lengths is

(A) 2a2c/b (B) 3a/2b2c (C) 2ac/b2 (D) 3c/2ab2

16

24. The pressure of a medium is changed from 1.01105 Pa to

1.165105 Pa and change in volume is 10% keeping temperature constant. The bulk modulus of the medium is

(A) 204.8105Pa (B) 102.4105Pa

(C) 51.2105Pa (D) 1.55105Pa 25. The string of a simple pendulum is replaced by a thin uniform

rod of mass M and length L. The mass of the bob is m. If it is allowed to oscillate with small amplitude, the period of oscillation is:

(A) 2(M + 3m)L

23(M + 2m)g

(B) 3(M + 2m)L

22(M + 3m)g

(C) (M + 2m)L

2(M + 3m)g

(D) 2(M + m)L

23(M + 2m)g

26. A mass hangs at the end of a massless spring and oscillates

up and down at its natural frequency f. if the spring is cut at the midpoint and the mass reattached at the end, the frequency of oscillation is

(A) 2f (B) 2 f

(C) f /2 (D) f / 2

27. A particle undergoes SHM of time period 2 seconds. In what

time will it move from an extreme position to a displacement equal to half of its amplitude?

(A) 1/2 s (B) 1/3 s (C) 1/4 s (D) 1/6 s 28. Two wires A and B are made of same material. The wire A has

a length and diameter r while the wire B has a length 2 and diameter r/2. If the two wires are stretched by the same force, the elongation in A divided by the elongation in B is :

(A) 1/8 (B) 1/4 (C) 4 (D) 8

29. The angular frequency of motion whose equation is

2d y4

dt +

9y = 0 is (y = displacement and t = time)

(A) 9

4 (B)

4

9

(C)3

2 (D)

2

3

30. The potential energy of a simple harmonic oscillator of mass 2

kg in its mean position is 5 J. If its total energy is 9J and its amplitude is 0.01 m, its time period would be

(A) /10 sec (B) /20 sec

(C) /50 sec (D) /100 sec

17

CHEMISTRY

31. The correct stability order for the following species as:

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

32. Among the following the least stable resonance structure is: (A) (B)

(C) (D)

33. The correct order for homolytic bond dissociation energies

( in kcal/mol) of C-H bond( of underlined H) for 4CH (A),

2 6C H (B) and 3 3CH C CH (C)2H , under identical experimental

conditions: (A) C B A (B) B C A

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

34. Which of the following resonating structures of 1-methoxy-1, 3-

butadiene is least stable?

(A) 2 3CH CH CH CH O CH

(B) 2 2 3CH CH CH CH O CH

(C) 2 3CH CH CH CH O CH

(D) 2 3CH CH CH CH O CH

35. The increasing order of stability of the following free radicals is

(A) (CH3)2C H < (CH3)3C < (C6H5)2 C H < (C6H5)3 C

(B) (C6H5)2 C < (C6H5)2 C H < (CH3)3 C < (CH3)2C H

(C) (C6H5)2 C H < (C6H5)3 C H < (CH3)3C < (CH3)2C H

(D) (CH3)2C H < (CH3)3C < (C6H5)3 C < (C6H5)2C H

O

(I)

(II)

O

(III)

(IV)

18

36. Consider the following carbocation,

(I) 6 5 2C H CH

(II) 6 5 2 2C H CH CH

(III) 6 5 3C H CHCH

(IV) 6 5 3 2C H C(CH )

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

37. Most stable carbonium ion is:

(A) 2 5C H

(B) 3 3(CH ) C

(C) 6 5 3(C H ) C

(D) 6 5 2C H CH

38. The total number of cyclic isomers possible for a hydrocarbon

with the molecular formula 4 6C H is:

(A) 1 (B) 3 (C) 5 (D) 7

39. The structure 3 3 3 2 3(CH ) CBr and CH [CH ] Br represent:

(A) Chain isomerism (B) Position isomerism (C) Chain as well as position isomerism (D) Functional isomerism

40. The alkene that exhibits geometrical isomerism is: (A) propene (B) 2-methyl propene (C) 2-butene (D) 2-methyl-2-butene

41. The number of isomeric alkanes having the molecular formula

5 12C H is:

(A) Three (B) Five (C) Nine (D) Thirty two

42. The number of possible alkynes with molecular formula 5 8C H

is: (A) 3 (B) 4 (C) 5 (D) 6

43. Metamers of ethyl propionate are:

(A) 4 9 4 9C H COOH and HCOOC H

(B) 4 9 3 3 7C H COOH and CH COOC H

(C) 3 3 3 3 7CH COOCH and CH COOC H

(D) 3 3 7 3 7 3CH COOC H andC H COOCH

19

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

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

45. Hydrogen molecule differs from chlorine molecule in the following respect. (A) hydrogen molecule is non-polar but chlorine molecule is polar (B) Hydrogen molecule is polar while chlorine molecular is non polar (C) Hydrogen molecule can form intermolecular hydrogen bonds but chlorine molecule does not (D) Hydrogen molecule cannot participate in coordinate bond formation but chlorine molecule can

46. Radioactive isotope of hydrogen is: (A) tritium (B) deuterium (C) parap hydrogen (D) ortho hydrogen

47. A reversible chemical reaction is having two reactants, in equilibrium. If the concentration of the reactants are doubled then the equilibrium constant will: (A) be doubled (B) become one fourth (C) be halved (D) remain the same

48. The buffering action of an acidic buffer is maximum when its pH is equal to: (A) 5 (B) 7

(C) 1 (D) apK

49. A solid is made of two elements X and Z. The atom Z are in

ccp arrangement while the atom X occupy all the tetrahedral sites. What is the formula of the compound?

(A) XZ (B) 2XZ

(C) 2X Z (D) 2 3X Z

20

50. Consider the following gaseous equilibria with equilibrium

constants 1 2K and K respectively.

2 2 31

SO (g) O (g) SO (g)2

3 2 22SO (g) 2SO (g) O (g)

The equilibrium constants are related as:

(A) 21 22K K (B) 2

12

1K

K

(C) 22

1

1K

K (D) 2 2

1

2K

K

51. If in the reaction 2 4 2N O 2NO ,x is that part of 2 4N O

which dissociates, then the number of molecules at equilibrium will be: (A) 1 (B) 3

(C) 1 x (D) 2(1 x)

52. A vessel at 1000 K contains 2CO with a pressure of 0.5 atm.

Some of the 2CO is converted into CO on the addition of

graphite. If the total pressure at equilibrium is 0.8atm, the

value of pK is:

(A) 1.8atm (B) 3atm (C) 0.3atm (D) 0.18atm

53. An acid HA ionizes as,

H.A H A

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

(A) 101 10 (B) 5

(C) 85 10 (D) 51 10

54. 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

21

55. A solid has a structure in which „W‟ atoms are located at the

corners of a cubic lattice „O‟ atoms at the centre of edge and Na atoms at the centre of cube. The formula for the compound is:

(A) 2 3Na WO (B) 2 2Na WO

(C) 2NaWO (D) 3NaWO

56. What is the coordination number of body centered cubic

crystal ? (A) 8 (B) 6 (C) 4 (D) 12

57. Which of the following has most acidic hydrogen? (A) 3-hexanone (B) 2, 4-hexanedione (C) 2,4-hexanedione (D) 2,3-hexanedione

58. The correct acidity order of the following is:

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

59. Given,

The decreasing order of the acidic character is: (A) A>B>C (B) B>A>C (C) B>C>A (D) C>B>A

60. Which of the following is most basic? (A) (B) (C) (D)

22

MATHEMATICS 61. 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) 112

11 (B)

112 1

11

(C) 113

11 (D)

113 1

11

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

all the girls are to stand together but the boys cannot all stand together? (A) 172,800 (B) 432,000 (C) 86,400 (D) none of these

63. There are three coplanar parallel lines. If any n points are taken on each of the lines, the maximum number of triangles with vertices at these points will be

(A) 23n n 1 (B) 23n n 1 1

(C) 2n 4n 3 (D) none of these

64. The letters of word “RADHIKA” are permuted are arranged in

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

65. If mth term of a HP be n and nth term be m, then the (mn)th terms is:

(A) m n

mn (B)

mn

m n

(C) 1 (D) m n

66. The third term of a GP is 4. Then the product of the first five

terms is

(A) 34 (B) 54

(C) 44 (D) 64

67. The nth term of a GP is 128, the sum of its first n terms is 225 and the common ratio is 2. The first term is (A) 32 (B) 31 (C) 8 (D) none of these

23

68. The sum 3 3 3 3 3 3

3 5 7....

1 1 2 1 2 3 upto 11 terms is

equal to

(A) 134

63 (B)

143

36

(C) 163

43 (D)

123

41

69. If n

n rr 1

S T n n 1 n 2 n 3 , then 10

rr 1

1

T is equal

to

(A) 55

527 (B)

58

528

(C) 59

528 (D) none of these

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

2 21 2z z 4 , then the value of

221 1 2 2z z z z is equal

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

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

1 1 1 1

1 1 1 1is

(A) 3

(B) 42

(C) 22 (D)

72. If z x iy z x iy then the equation2z i

mz 1

does not

represent a circle when

(A) 1

m2

(B) m =1

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

73. If10 10

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

(A) 2

(B)

(C)4

(D) none of these

74. A double ordinate of the parabola 2y 8px is of length 16p.

The angle subtended by it at the vertex of the parabola is

(A) /4 (B) /2

(C) (D) /3

24

75. If the vertex of the parabola 2y x 8x c lies on x-axis,

then the value of c is (A) 16 (B) 4

(C) 16 (D) none of these

76. The equation 2 2x 4xy 4y 4x 4y 0 will represent

a parabola

(A) for all values of

(B) for all except for one value of

(C) for no values of (D) none of these

77. A teacher takes 3 children from her class to the zoo at a time

as often as she can, but she does not take the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class is (A) 12 (B) 10 (C) 60 (D) none of these

78. Equation of straight line whose intercepts on x-axis and y-axis

are respectively twice and thrice of those by the line 3x 4y 12 is

(A) 9x 8y 72 (B) 9x 8y 72

(C) 3x 4y 72 (D) none of these

79. Points A and B are in the first quadrant. Point O is the origin. If

the slope of OA is 1, slope of OB is 7 and OA OB , then

slope of AB is:

(A) 1

5 (B)

1

4

(C) 1

3 (D)

1

2

80. The area of triangle formed by the lines x y 3 0 ,

x 3y 9 0 and 3x 2y 1 0 is

(A) 16

7sq. units (B)

10

7 sq. units

(C) 4 sq. units (D) 9 sq. units

81. A stick of length 10units rest against the floor and a wall of a room. If the stick begin to slide on the floor, then the middle point of a stick always lies on:

(A) 2 2 5x y

2 (B) 2 2x y 25

(C) 2 2x y 100 (D) none of these

25

82. Through a point A on the x-axis a straight line drawn parallel to y-axis so as to meet the pair of straight lines

2 2ax 2hxy by 0 in B and C. If AB BC , then

(A) 2h 4ab (B) 28h 9ab

(C) 29h 8ab (D) 24h ab

83. 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

84. 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

85. 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

86. The sum of values of p such that the vertex of

2y x 2px 13 is 4 unit above the x-axis is

(A) 0 (B) 1

(C) 2 (D) 3

87. A point P on a parabola 2y 4x , the foot of the perpendicular

from it upon the directrix and the focus are the vertices of an equilateral triangle, the area of the equilateral triangle is

(A) 4 3 (B) 2 3

(C) 4 3

5 (D)

5

4 3

88. If the coefficient of 7x and 8x in the expansion of n

x2

3

are equal, then the value of n is: (A) 15 (B) 45 (C) 55 (D) 56

26

89. 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

90. 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) 28 (D) 32