MATHS

1. If 2x2 – 10xy + 2y2 + 5x – 16y – 3 = 0 represents a pair of straight lines, then point of intersection of those lines is

1) (2, –3) 2) (5, –16) 3) 710,2

4) 310,

2

Key-3 2. A village has 10 players, A team of 6 players is to be formed. 5 members are chosen first out of these 10

players and then the captain is chosen from the remaining players. Then the total number of ways of choosing such team is

1) 1260 2) 210 3) ( 106C )5! 4) ( 10

5C )6! Key-1 3. If f is differentiable, f x y f x f y for all x,y R, f(3)=3, f’(0)=11, then f’(3)=

1) 311

2) 113

3) 8 4) 33

Key-4 4. A point on the plane that passes through the points (1,-1,6), (0,0,7) and perpendicular to the plane x-2y+z=6

is 1) (1, - 1,2) 2) (1,1,2) 3) (-1,1,2) 4) (1,1,-2) Key-2 5. For the parabola 2 6 2 5y y x I) The vertex is (-2,-3) II) The directrix is y+3=0 Which of the following is correct? 1) Both I and II are correct 2) I is true, II is false 3) Both I and II are false 4) I is false, II is true Key-2

6. 1 13 2sin sin2 3

1) 1 3 2sin2 3

2) 1 3 2sin

2 3

3) 1 3 2sin2 3

4) 1 3 2sin

2 3

Key-2 7. Let 2 3a i j k

and 3 2b i j k

. Then the volume of the parallelepiped having conterminous edges

as ,a b and c

, where c

is the vector perpendicular to the plane of a

, b

and c

=2 is

1) 2 195 2) 24 3) 200 4) 195 Key-1

8. The sum of the complex roots of the equation 31 64 0x is 1) 6 2) 3 3) 6i 4) 3i Key-2

9. If 1 2tan cot ,k then

1 2

1 2

coscos

1) 11

kk

2) 11

kk

3) 11

kk

4) 11

kk

Key-2 10. A parallelogram has vertices A(4, 4, -1), B(5,6,-1) C(6, 5, 1) and D(x, y, z). Then vertex D is 1) (5, 1, 0) 2) (-5, 0, 1) 3) (5, 3, 1) 4) (5, 1, 3) Key-3 11. The solution of 23 0y x dx xdy is

1) 2

1siny x x Cx

2) 2

1cosy x x Cx

3) 2 Cy x xx

4) Cy x xx

Key-3 12. In ,ABC if 01, 2, 60a b C then 2 24 c

1) 6 2) 3 3) 32

4) 9

Key-1

13. 2 20 4cos 9sin

xdxx x

1) 2

12

2) 2

4

3) 2

6

4) 2

3

Key-1 14. The lengths of the sides of a triangle are 13, 14 and 15. If R and r respectively denote the circum radius

and inradius of that triangle, then 8R + r =

1) 84 2) 658

3) 4 4) 69

Key-4

15. The product of all the real roots of 22

8 18 9 0x xx x

is

1) 2 2) 1 3) 3 4) 7 Key-2

16. If 1 5 60 1 70 0 1

and 1

1 0 13 0 34 6 100

, then

1) 2 13 0 2) 21 13 2 0

3) 21 13 5 0 4) 13 1 0 Key-2 17. If the vectors ,a i j k

2b i j k

and 2c xi x j k

are coplanar, then x

1) 1 2) 2 3) 0 4) -2 Key-4

18. If a

, b

and c

are unit vectors such that 0a b c

and ,3

a b

, then a b b c c a

1) 32

2) 0 3) 3 32

4) 3

Key-3 19. Two circles of equal radius ‘a’ cut orthogonally. If their centres are (2, 3) and

(5, 6) then radical axis of these circles passes through the point

1) (3a, 5a) 2) (2a, a) 3) 5,3aa

4) (a, a)

Key-3

20. For any integer 1

1, 2n

Kn K K

1) 1 2

6n n n

2) 1 2 7

6n n n

3) 1 2 1

6n n n

4) 1 2 8

6n n n

Key-2 21. Consider the circles x2 + y2 – 6x + 4y = 12. The equation of a tangent to this circle that is parallel to the

line 4x + 3y + 5 = 0 is 1) 4x + 3y + 10 = 0 2) 4x + 3y – 9 = 0 3) 4x + 3y + 9 = 0 4) 4x + 3y – 31 = 0 Key-4 22. Match the following List – I List – II

i) 1

1x x dx

a) 2

ii) 20

4 3sin1 log4 3cos

x dxx

b) 2

0

a

f x dx

iii) 0

af x dx c)

0

af x f x dx

iv) a

af x dx

d) 0

e) 0

af a x dx

I II III IV I II III IV (1) d a e c (2) d a c b (3) d c a e (4) a d b c

Key-1

23. 1 cos sin

12 12

1 cos sin12 12

i

i

1) zero 2) –1 3) 1 4) 12

Key-3

24. If and are the roots of the equation ax2 + bx + c = 0 and the equation having roots 1 and

1

is px2 + qx + r = 0, then r = 1) a + 2b 2) ab + bc + ca 3) a + b + c 4) abc Key-3

25. If

2

22

52 11 2

x A Bx Cx xx x

then A + B + C =

1) –1 2) 25

3) 35 4) 0

Key-3

26. If the imaginary part of 2 11

ziz

is –2, then the locus of the point representing z in the complex plane is

1) a circle 2) a parabola 3) a straight line 4) an ellipse Key-3 27. The mean deviation from the mean 10 of the data 6, 7, 10, 12, 13, , 12, 16 is 1) 3.5 2) 3.25 3) 3 4) 3.75 Key-3 28. The angle between the curve x2 = 8y and xy = 8 is

1) 1 1tan3

2) 1tan 3 3) 1tan 3 4) 1 1tan3

Key-3

29. If 2 2

2 2 1,x ya b

then 2

2

d ydx

1) 4

2 3

ba y 2)

2

2

bay

3) 3

2 3

ba y 4)

3

2 2

ba y

Key-2 30. If the slope of the tangent to the curve y = ax3 + bx + 4 at (2, 14) is 21, then the value of a and b are

respectively. 1) 2, –3 2) 3, –2 3) –3, –2 4) 2, 3 Key-1

31. The solution of dy x ydx x y

is

1) 1 2 2tan logy x y Cx

2) 1 2 2tan logy x y Cx

3) 1 2 2sin logy x y Cx

4) 1 2 2cos logy x y Cx

Key-1 32. If the line x – y = –4k is a tangent to the parabola y2 = 8x at P, then the perpendicular distance normal at p

from (K, 2K) is

1) 5

2 2 2)

72 2

3) 9

2 2 4)

12 2

Key-3 33. If the pair of straight lines xy – x – y + 1 = 0 and the line x + ay – 3 = 0 are concurrent, then the acute

angle between the pair of lines ax2 – 13xy – 7y2 + x + 23y – 6 = 0

1) 1 5cos218

2) 1 1cos10

3) 1 5cos173

4) 1 1cos5

Key-2

34. 4 1

dxx x

1) 4

4

1 1log4

x Cx

2)

4

4

1 log4 1

x Cx

3) 41 log 14

x C 4) 4

4

1 log4 2

x Cx

Key-2 35. The local maximum of y = x3 – 3x2 + 5 is attained at 1) x = 0 2) x = 2 3) x = 1 4) x = –1 Key-1

36. If a

is a unit vector, then 2 2 2

a i a j a k

1) 2 2) 4 3) 1 4) 0 Key-1 37. The area of the region bounded between the curves x = y2 – 2, x = y is

1) 94

2) 9 3) 92

4) 97

Key-3 38. and are the roots of x2 + 2x + C = 0. If 3 3 4 , then the value of C is 1) –2 2) 3 3) 2 4) 4 Key-3 39. The equation of the straight line passing through the point of intersection of 5x – 6y – 1 = 0, 3x + 2y + 5 = 0 and perpendicular to the line 3x – 5y + 11 = 0 is

1) 5x + 3y + 18 = 0 2) –5x – 3y + 18 = 0 3) 5x + 3y + 8 = 0 4) 5x + 3y – 8 = 0 Key-3 40. The probability distribution of a random variable X is given below

X=k 0 1 2 3 4 P(X=k) 0.1 0.4 0.3 0.2 0

Then the variance of x is

1) 1.6 2) 0.24 3) 0.84 4) 0.75 Key-3

41. If 2 ' ,xe f x dx g x then 2 2 'x xe f x e f x dx

(1) 212

xe f x g x C (2) 212

xe f x g x C

(3) 21 22

xe f x g x C (4) 2 '1 22

xe f x g x C

Key-2 42. The sides of a triangle are in the ratio 1: 3 : 2 . Then the angles are in the ratio (1) 1:2:3 (2) 1:2:4 (3) 1:4:5 (4) 1:3:5 Key-1 43. If A and B are events having probabilities, P(A) = 0.6, P(B) = 0.4 and 0P A B , then the

probability that neither A nor B occurs is

(1) 14

(2) 1 (3) 12

(4) 0

Key-4 44. The probability distribution of a random variable X is given below:

If mean of X is 4.2, then a and b are respectively equal to (1) 0.3, 0.2 (2) 0.1, 0.4 (3) 0.1, 0.2 (4) 0.2, 0.1 Key-3 45. If the conjugate of 1 2x iy i is 1 i , then

(1) 1x iy i (2) 11 2

ix iyi

(3) 1

1 2ix iyi

(4) 1

1ix iyi

Key-2

46. If 0 0

00 0

tan160 tan110tan 20 , then1 tan160 tan110

X 1 2 3 4 5 6 P(X=x) a a a b b 0.3

(1) 21

2

(2) 21

(3)

21 (4)

212

Key-4 47. If ˆˆ ˆ ,a xi yj zk

then ˆ ˆ ˆˆ ˆ ˆ ˆ ˆ ˆ. . .a i i j a j j k a k k i

(1) x y z (2) x y z (3) x y z (4) x y z Key-2 48. A straight line makes an intercept on the Y-axis twice as long as that on X-axis and is at a unit distance

from the origin. Then the line is represented by the equations (1) 2 3 5x y (2) 2x y (3) 2x y (4) 2 5x y Key-4

49. If the line 0x y k is a normal to the hyperbola 2 2

19 4x y

then k =

(1) 513

(2) 135

(3) 135

(4) 513

Key-2 50. If the magnitudes of ,a b

and a b

are respectively 3, 4 and 5, then the magnitude of a b

is

(1) 3 (2) 4 (3) 6 (4) 5 Key-4 51. If 1cosh 2 log 2 1ex , then x =

(1) 1 (2) 2 (3) 4 (3) Key-4 52. An integer is choosen from 2 / 9 10k k . The probability that is divisible by both 4 and 6 is

(1) 110

(2) 120

(3) 14

(4) 320

Key-4

53. 2 41

1 21 1y

Limy y

(1) 12

(2) 13

(3) 14

(4) 0

Key-1 54. If 5,3 , 3, 2A B and a point P is such that the area of the triangle PAB is 9, then the locus of P

represents (1) a circle (2) a pair of coincident lines (3) a pair of parallel lines (4) a pair of perpendicular lines Key-3

55. If the range of the function 3 3f x x is 3, 6, 9, 18 , then which of the following elements is not in the domain of f ?

(1) -1 (2) -2 (3) 1 (4) 2 Key-1

56. If 2 2

sin 00 1

2 1 20 2

x if xx a if x

f xbx if x

if x

is continuous of , then a b ab

(1) -2 (2) 0 (3) 2 (4) -1 Key-4 57. If A and B are the variances of the 1st ‘n’ even numbers and 1st ‘n’ odd numbers respectively then (1) A=B (2) A>B (3) A<B (4) A=B+1 Key-1

58. If 21cos2

f x xdx f x C and 10 0, 0f then f

(1) 1 (2) -1 (3) 0 (4) 2 Key-1 59. The foci of the ellipse 2 225 4 100 4 100 0x y x y are

(1) 5 21 , 210

(2) 5 212,

10

(3) 2 21 , 210

(4) 2 212,

10

Key-2

60. If 1 0 10 2 0 , ,1 1 4

TA A B C B B

and ,TC C then C =

(1) 0 0.5 00.5 0 00 0 0

(2) 0 0 00 0 0.50 0.5 0

(3) 0 0.5 0.5

0.5 0 00.5 0 0

(4) 0 0.5 00.5 0 0.50 0.5 0

Key-2

61. If the slope of the tangent to the circle 2 2 13 0S x y at (2, 3) is m, then the point 1,mm

is

(1) an external point with respect to the circle S = 0

(2) an internal point with respect to the circle S = 0 (3) the centre of the circle S = 0 (4) a point on the circle S = 0 Key-2 62. The radical centre of the circles 2 2 2 2 2 24 6 5 0, 2 4 1 0, 6 2 0x y x y x y x y x y x y

lies on the line (1) 5 0x y (2) 2 4 7 0x y (3) 4 6 5 0x y (4) 18 12 1 0x y Key-4 63. Using the letters of the word TRICK, a five letter word with distinct letters is formed such that C is in

the middle. In how many ways this is possible? (1) 6 (2) 120 (3) 24 (4) 72 Key-3

64. The equation of tangent to the curve 2n nx y

a b

at the point ,a b is

(1) x ya b (2) 2x y

a b (3) x y

a b (4) x y n

a b

Key-2 65. If the coefficients of 2 1 thr term and 1 thr term in the expansion of 421 x are equal then r can be (1) 12 (2) 14 (3) 16 (4) 20 Key-2 66. In the expansion of 1 ,nx the coefficients of pth and (p+1)th terms are respectively p and q, then p+q = (1) 3n (2) 2n (3) n (4) 1n Key-4 67. If : ( , 0] [0, )f is defined as 2f x x . The domain and range of its inverse is

(1) Domain of 1 1[0, ), ( ,0]f Rangeof f

(2) Domain of 1 1[0, ), ( , )f Rangeof f

(3) Domain of 1 1[0, ), [0, )f Rangeof f (4) 1f does not exist Key-1

68. If rank of 2

1

x x xx x xx x x

is 1, then

(1) 0 1x or x (2) 1x (3) 0x (4) 0x Key-3 69. The differential equation of the simple harmonic motion given by cosx A nt is

(1) 2

22 0d x n x

dt (2)

22

2 0d x n xdt

(3) 2

2 0dx d xdt dt

(4) 2

2 0d x dx nxdt dt

Key-2 70. If a

and b

are unit vectors and is the angle between them, then a b

is a unit vector when cos

(1) 12

(2) 12

(3) 32

(4) 32

Key-1 71. Let : 1,1f be a differentiable function with 0 1f and ' 0 1f . If 2

2 2g x f x ,

then ' 0g (1) 0 (2) -2 (3) 4 (4) -4 Key-4 72. The number of solutions of cos2 sin in 0,2 is (1) 4 (2) 3 (3) 2 (4) 5 Key-2 73. If cosec cot 2017, then the quadrant in which lies is (1) I (2) IV (3) III (4) II Key-4 74. In order to eliminate the first degree terms from the equation 2 24 8 10 8 44 14 0x xy y x y the point

to which the origin has to be shift (1) (-2, 3) (2) (2, -3) (3) (1, -3) (4) (-1, 3) Key-1 75. 4 2xx e dx

(1) 2

4 3 22 4 6 6 34

xe x x x x C (2) 2

4 3 22 4 6 6 32

xe x x x x C

(3) 2

4 3 22 4 6 6 38

xe x x x x C (4) 2

4 3 22 4 6 6 34

xe x x x x C

Key-1 76. If the perpendicular distance between the point (1, 1) to the line 3 4 0x y c is 7, then the possible

values of c are (1) -35,42 (2) 35, 28 (3) 42, -28 (4) 28, -42 Key-4

77. If ,3 6

A B

are the points on the circle represented in parametric from with centre (0, 0) and radius

12 then the length of the chord AB is (1) 6 6 2 (2) 6 6 3 (3) 2 3 1 (4) 6 3 1

Key-1 78. Let f x be a quadratic expression such that 0 1 0f f . If 2 0f , then

(1) 2 05

f

(2) 2 05

f

(3) 3 05

f

(4) 3 05

f

Key-4 79. Let S and S1 be the foci an ellipse and B be one end of its minor axis. If SBS1 is an isosceles right angled

then the eccentricity of the ellipse is

(1) 12

(2) 12

(3) 32

(4) 13

Key-1 80. A bag contains 5 red balls, 3 black balls and 4 white balls. Three balls are drawn at random. The probability

that they are not of same colour is

(1) 3744

(2) 3144

(3) 2144

(4) 4144

Key-1 PHYSICS

81. A parallel beam of light of intensity 0I is incident on a coated glass plate. If 25% of the incident light is reflected from the upper surface and 50% of light is reflected from the lower surface of the glass plate, the ratio of maximum to minimum intensity in the interference region of the reflect light is

(1)

21 32 81 32 8

(2)

21 34 81 32 8

(3) 58

(4) 85

Key-1 82. A wire has resistance of 3.1 at 30C and 4.5 at 100C. The temperature coefficient of resistance of

the wire is

(1) 10.0012 C (2) 10.0024 C (3) 10.0032 C (4) 10.0064 C

Key-0

83. The Young’s modulus of a material is 11 22 10 /N m and its elastic limit is 8 21 10 /N m . For a wire of 1 m length of this material, the maximum elongation achievable is

(1) 0.2 mm (2) 0.3 mm (3)0.4 mm (4) 0.5 mm Key-4 84. A sound wave of frequency ‘ ’ Hz initially travels a distance of 1 km in air. Then it gets reflected into a

water reservoir of depth 600 m. The frequency of the wave at the bottom the reservoir is 340 / ; 1484 /air waterV m s V m s .

(1) > Hz (2) < HZ (3) Hz (4) 0 (the sound wave gets attenuated by water complete). Key-3 85. Which of the following principles is being used in Sonar Technology ? (1) Newton’s laws of motion (2) Reflection of electromagnetic waves (3) Laws of thermodynamics (4) Reflection of ultrasonic waves

Key-4 86. A ball is thrown at a speed of 20 m/s at an angle of 30 with the horizontal. The maximum height reached

by the ball is (use 210 /g m s )

(1) 2m (2) 3 m (3) 4 m (4) 5 m Key-4 87. A swimmer wants to cross a 200 m wide river which is flowing at a sped of 2m/s. The velocity of the

swimmer with respect to the river is 1m/s. How far from the point directly opposite to the starting point does the swimmer reach the opposite bank?

(1) 200 m (2) 400 m (3) 600 m (4) 800 m Key-2

88. A beam of light propagating at an angle 1 from a medium 1 through to another medium 2 at an angle 2 . If the wavelength of light in medium 1 is 1 , the wavelength of light in medium 2, 2 is

(1) 2

1

inS sSin

(2) 11

2

inSSin

(3) 11

2

(4) 1

Key-1 89. A horizontal pipeline carrying gasoline has a cross-sectional diameter of 5 mm. if the viscosity and density

of the gasoline are 36 10 Poise and 720 2/kg m respectively, the velocity after which the flow become turbulent is

(1) > 1.66 m/s (2) > 3.35 m/s (3) 31.6 10 /m s (4) > 0.33 m/s Key-4 90. Consider a light source placed at a distance of 1.5 m along the axis facing the convex side of a spherical

mirror of radius of curvature 1m. The position 's , nature and magnification (m) of the image are

(1) ' 0.375 ,s m Virtual, upright m = 0.25 (2) ' 0.375 ,s m Read, inverted, m = - 2.5

(3) ' 3.75 ,s m Virtual, inverted, m = 2.5 (4) ' 3.75 ,s m , Read, upright, m = 2.5

Key-1

91. Consider a particle on which constant forces 1 ˆˆ ˆ2 3F i j k N

and 2 ˆˆ ˆ4 5 2F i j k

N act together resulting in a displacement from position 1 ˆ ˆ20 15r i j

cm to 2 ˆ7r k

cm. The total work done on the

particle is (1) – 0,48 J (2) + 0.48 J (3) – 4.8 J (4) + 4.8 J Key-1

92. An office room contains about 2000 moles of air. The change in the internal energy of this much air when it is cooled from 34 C to 24 C at a constant pressure of 1.0 atm is [Use 1.4air and Universal gas constant = 8.314 J/mol K]

(1) 51.9 10 J (2) 51.9 10 J (3) 54.2 10 J (4) 50.7 10 J Key-3 93. A piece of copper and a piece of germanium are cooled from room temperature to 80 K. Then, which one

of the following is correct? (1) Resistance of each will increase (2) Resistance of each will decrease (3) Resistance of copper will decrease while that of germanium will increase (4) Resistance of copper will increase while that of germanium will decrease Key-3 94. Consider a frictionless ramp on which a smooth object is made to slide down from air initial height ‘h’. The

distance ‘d’ necessary to stop the object on a flat track (of coefficient of friction ' ' ), kept at the ramp end is

(1) /h (2) h (3) 2h (4) 2h

Key-1 95. A wooden box lying at rest on an inclined surface of a wet wood is held at static equilibrium by a constant

force F

applied perpendicular to the incline. If the mass of the box is 1 kg, the angle of inclination is 30 and the coefficient of static friction between the box and the inclined plane is 0.2, the minimum magnitude of F

is (Use 210 /g m s ).

(1) 0 N, as 30 is less than angle of repose (2) 1N (3) 3.3N (4) 16.3 N

Key-4 96. An electron collides with a Hydrogen atom in its ground state and excites it to n =3 state. The energy given

to the Hydrogen atom in this inelastic collision (neglecting the recoil of Hydrogen atom) is (1) 10.2 eV (2) 12.1 eV (3) 12.5 eV (4) 13.6 Ev Key-2 97. A planet of mass ‘m’ moves in an elliptical orbit around an unknown star of mass ‘M’ such that its maximum

and minimum distances from the star are equal to 1 2r and r respectively. The angular momentum of the planet relative to the centre of the star is

(1) 1 2

1 2

2GMr rmr r

(2) 0 (3) 1 2

1 2

2GM r rm

r r

(4) 1

1 2 2

2GMmrmr r r

Key-1

98. A simple pendulum of length 1m is freely suspended from the celling of an elevator. The time period of small oscillation as the elevator moves up with an acceleration of 22 /m s is (use 210 /g m s )

(1) 5

s (2) 25

s (3) 2

s (4) 3

s

Key-4 99. A meter scale made of steel reads accurately at 25 C . Suppose in an experiment an accuracy of 0.06 mm

in 1m is required, the range of temperature in which the experiment can be performed with this metre scale is (coefficient of linear expansion of steel is 611 10 / C ).

(1) 19 31C to C (2) 25 12C to C (3) 25 12C to C (4) 18 32C to C

Key-1

100. A positive charge ‘Q’ is placed on a conducting spherical shell with inner radius 1R and outer radius 2R . A particle with charge ‘q’ is placed at the center of the spherical cavity. The magnitude of the electric field at a point in the cavity, a distance ‘r’ from center is

1) zero 2) 204

QR

3) 204

qR

4)

204

q QR

Key-3 101. An AC generator producing 10 V (rms) at 200 rad/s is connected in series with a 50 resistor, a 400

mH induction and 200 F capacitor. The rms voltage across the inductor is

1) 2.5 V 2) 3.4 V 3) 6.7 V 4) 10.8 V

Key-4 102. A particle of mass M is moving in a horizontal circle of radius R with uniform speed. When the particle

moves from one point to a diametrically opposite point, its

1) momentum does not change 2) momentum changes by 2 MV

3) kinetic energy changes by 2

4Mv 4) kinetic energy changes by 2Mv

Key-2

103. Consider a reversible engine of efficiency 16

. When the temperature of the sink is reduced by 062 C , its

efficiency gets doubled. The temperature of the source and sink respectively are

1) 372 K and 310 K 2) 273 K and 300 K 3) 990C and 100C 4) 2000C and 370C

Key-1

104. A generator with a circular coil of 100 turns of area 2 22 10 m is immersed in a 0.01 T magnetic field and rotated at a frequency of 50 Hz. The maximum emf which is produced during a cycle is

1) 6.28 V 2) 3.44 V 3) 10 V 4) 1.32 V

Key-1 105. A force F

is applied on a square plate of length L. If the percentage error in the determination of L is

3% and F is 4%, the permissible eror in the calculation of pressure is

1) 13% 2) 10% 3) 7% 4) 12%

Key-2 106. Consider a metal ball of radius ' 'r moving at a constant velocity ' 'v in a uniform magnetic field of

induction B . Assuming that the direction of velocity forms an angle ' ' with the direction of B ,t he maximum potential difference between points on the ball is

1) r B v Sin 2) B v Sin 3) 2r B v Sin 4) 2r B v Cos

Key-3 107. Which of the following statement is not true ?

1) the resistance of an intrinsic semiconductor decreases with increase in temperature

2) doping pure Si with trivalent impurities gives p-tyres semiconductor

3) the majority carriers in n-type semiconductors are holes

4) a p – n junction can act as a semiconductor diode

Key-3 108. Each of the six idal batteries of emf 20V is connected to an external resistance of 1 as shown in the

figure. The current through the resistance is (diagram)

80 C

4 F

3 F2 F

1) 6A 2) 12A 3) 4A 4) 5A

Key-0

109. An object is thrown vertically upward with a speed of 30 m/s. The velocity of the object half – a- second before it reaches the maximum height is

1) 4.9 m/s 2) 9.8 m/s 3) 19.6 m/s 4) 25.1 m/s

Key-1 110. In the given circuit, a charge of +80 C is given to upper plate of a 4 C capacitor. At steady state the

charge on the upper plate of the 3 C capacitor is

R = 4

1) 69 C 2) 48 C 3) 80 C 4) 0 C

Key-2 111. The energy that should be added to an electron to reduce its de-Broglie wavelength from 1 nm to 0.5

mm is

1) four-times the initial energy 2) equal to the initial energy

3) two – times the initial energy 4) three – times the initial energy

Key-4 112. A thermocol box has a total wall area (including the lid ) of 1.0 m2 and wall thickness of 3cm. It is

filled with ice at 00C. If the average temperature outside the box is 300C throughout the day, the amount of ice melts in one day is

[ use Kthermocol = 0.03 W / m K, L fussion(ice) = 3.00 x 105 J/Kg]

1) 1kg 2) 2.88 kg 3) 25.92 kg 4) 8.64 Kg

Key-4 113. The declaration of car travelling on a straight highway is a function of its instantaneous velocity ' 'v

given by ,w a v where ' 'a is constant. If the initial velocity of the car is 60 km/hr, the distance the car will travel and the time it takes before it stops are

1) 2 1,3 2

m s 2) 2 1,2 2

m sa a

3) 3 ,2 2a am s 4) 2 2,

3m s

a a

Key-0

114. Consider the motion of a particle described by cos ,x a t siny a t and z t . The trajectory traced by the particle as a function of time is

1) Helix 2) Circular 3) Elliptical 4) Straight line

Key-1 115. An amplitude modulated signal consists of massage signal of frequency 1 kHz and peak voltage of 5V,

modulating a carrier frequency of 1 MHz and peak voltage of 15 V. The correct description of this signal is

1) 6 35 1 3sin 2 10 sin 2 10t t 2) 3 6115 1 sin 2 10 sin 2 103

t t

3) 3 61 15sin 2 10 sin 2 10t t 4) 6 315 5sin 2 10 sin 2 10t t

Key-2 116. A current carrying wire in it neighbourhood produces

1) electric field 2) electric and magnetic fields 3) magnetic field 4) no field

Key-3 117. A coil having ' 'n turns and resistance R is connected with a galvanometer of resistance 4R . This

combination is moved in time v seconds from a magnetic flux 1 and 2 Weber. The induced current in the circuit is

1) 2 1

5Rnt 2) 2 1

5n

Rt

3) 2 1

Rnt

4) 2 1nRt

Key-2 118. A billiard ball of mass ' 'M moving the velocity ' 'tv collides with another ball of the same mass but at

rest. If the collision is elastic the angle of divergence after the collision is

1) 00 2) 030 3) 090 4) 045

Key-1,3 119. Consider a solenoid carrying current supplied by a DC source with a constant emf containing iron core

inside it. When the core is pulled out of the solenoid, the change in current will

1) remain same 2) decrease 3) increase 4) modulate

Key-3 120. Which of the following is emitted when 219

94 Pu decays into 23592 U ?

1) Gamma Ray 2) Neutron 3) Electron 4) Alpha particle

Key-4

CHEMISTRY 121. Which of the following statement is true 1) The presseure of a fixed amount of an ideal gas is proportional to its temperature on 2) Frequency of collisions increases in proportion to the square root of temperature 3) The value of vander Waals constant ‘a’ is smaller for ammonia than for nitrogen 4) If a gas is expanded at constant temperature, the kinetic energy of the molecule decrease. Key-2 122. Conversion of esters to aldehydes can be accomplished by 1) Stephen reduction 2) Rosenmund reduction 3) Reduction with lithium aluminium hydride 4) reduction with diisobutyl aluminimum hydride Key-4 123. Heating a mixture of 2Cu O and 2Cu S will give ? 1) CuO CuS 2) 3Cu SO

3) 2Cu SO 4) 42Cu OH CuSO

Key-3 124. Which of the following conditions are correct for real solutions showing negative deviation from Raoult’s

law ? 1) mix mixH 0; V 0 2) mix mixH 0; V 0 3) mix mixH 0; V 0 4) mix mixH 0; V 0 Key-4 125. Which of the following is the most basic oxide ? 1) 3SO 2) 3SeO 3) PoO 4) TeO Key-3

126. Standard Enthalpy (Heat) of formation of liquid water at 250C is around 2 2 2g g l1H O H O2

1) -237 kJ / mol 2) 237 kJ / mol 3) -286 kJ/mol 4) 286 kJ /mol Key-3 127. The alcohol that reacts faster with Lucas reagent is

1) 3 2 2 2CH CH CH CH OH 2) 3 2 3CH CH CH CH

| OH

3) 3 2

3

CH CH CH OH | CH

4)

3

3

3

CH |CH C OH | CH

Key-4 128. Balance the following equation by choosing the correct option

3 12 22 11 2 2 2 2 3xKNO yC H O pN qCO rH O sK CO

X Y P Q R S 1 36 55 24 24 5 48 2 48 5 24 36 55 24 3 24 24 36 55 48 5 4 24 48 36 24 5 55

Key-2 129. Which of the following corresponds to the energy of the possible excited state of hydrogen ? 1) -13.6 eV 2) 13.6 eV 3) -3.4 eV 4) 3.4 eV Key-3 130. Consider the single electrode process 24H 4e 2H catalyzed by platinum black electrode in HCl

electrolyte. The potential of the electrode is -0.059V Vs. SHE. What is the concentration of the acid in the hydrogen half cell if the H2 pressure is 1 bar ?

1) 1M 2) 10 M 3) 0.1 M 4) 0.01 M Key-3 131. When helium gas is allowed to expand in to vaccum, heating effect is observed. The reason for this is

(Assume He as a non ideal gas) 1) He is an inert gas 2) The inversion temperature of Helium is very high 3) The inversion temperature of Helium is very low 4) He has the lowest boiling point Key-3

132. Consider the following electrode processes of a cell, 21Cl Cl e2

, MCl e M Cl

If EMF of this cell is – 1.140 V and E value of the cell is – 0.55 V at 298 K, the value of the equilibrium constant of the sparingly soluble salt MCl is in the order of 1) 1010 2) 810 3) 710 4) 1110

Key-1 133. Cyhclopentadienyl anion is 1) benzenoid and aromatic 2) non-benzenoid and aromatic 3) non-benzenoid and non-aromatic 4) non-benzenoid and anti-aromatic Key-2 134. Given 0

fH for 2 gCO , gCO , abd 2 gH O are -393.5, -110.5 and -241.8 kJ mol-1, respectively. The 0fH [in kJ mol-1] for the reaction 2 2 2g g g gCO H CO H O is

1) 524.1 2) -262.5 3) -41.7 4) 41.2 Key-4 135. The number of tetrahedral and octahedral voids in CCP unit cell are respectively 1) 4, 8 2) 8, 4 3) 12, 6 4) 6, 12 Key-2 136. Which of the following element is purified by vapour phase refining ? 1) Fe 2) Zr 3) Cu 4) Au

Key-2 137. The electro nic configuration of 59 Pr (praseodymium) is 1) 2 1 2

54 Xe 4f 5d 6s 2) 1 2 254 Xe 4f 5d 6s

3) 3 254 Xe 4f 6s 4) 3 2

54 Xe 4f 5d Key-3 138. The vapour pressure of a non-ideal two component solution is given below : Identify the correct T-X curve for the same mixture,

800

600

400

200

0 0.5 1.0

X

pmmHg

1)

0 0.5 1

X

B.P (K)

2)

0 0.5 1

X

B.P (K)

3)

0 0.5 1

X

B.P (K)

4)

0 0.5 1

X

B.P (K)

Key-1 139. The bond length (pm) of 2 2 2F ,H ,Cl and 2I respectively is 1) 144, 74, 199, 267 2) 74, 144, 199, 267 3) 74, 267, 199, 144 4) 144, 74, 267, 199 Key-1 140. The bonding in diborane (B2H6) can be described by; -

1) 4 two centre – two electron bonds & 2 three – centre – two electron bonds 2) 3 two centre – two electron bonds & 3 three centre – two electron bonds 3) 2 two centre – two electron bonds and 4 three centre - two electron bonds 4) 4 two centre – two electron bonds and 4 two centre - two electron bonds Key-1 141. The element that forms stable compounds in low oxidation state is 1) Mg 2) Al 3) Ga 4) Tl Key-4 142. Oxidation of cyclohexene in presence of acidic potassium permanganate leads to 1) glutaric acid 2) adipic acid 3) pimelic acid 4) succinic acid Key-2

143. Optically active

3 2 3

OH |CH CH CH CH

was found to have lost its optical activity after standing in water

containing a few drops of acid, mainly due to the formation of 1) 3 2 2CH CH CH CH 2) 3 3CH CH CH CH

3) 3

3 2

CH |CH CH CH OH

4) 3 2 2 2CH CH CH CH OH

Key-2 144. How many emission spectral lines are possible when hydrogen atom is excited to nth energy level?

1) n n 12

2) n 12

3) n 1 n2

4) 2n

4

Key-3 145. The monomers of Buna-S rubber are 1) Isoprene and butadiene 2) Butadiene and phenol 3) Styrene and butadiene 4) Vinyl chloride and sulphur Key-3 146. Atomic radius (pm) of Al, Si, N and F respectively is 1) 117, 143, 64, 74 2) 143, 117, 74, 64 3) 143, 47, 64, 74 4) 64, 74, 117, 143 Key-2 147. Which of the following elements has the lowest melting point ? 1) Sn 2) Pb 3) Si 4) Ge Key-1 148. ____ is a potent vasodilator 1) Histamine 2) Serotonin 3) Codeine 4) Cimetidine Key-1 149. The number of complementary Hydrogen bond(s) between a guanine and cytosine pair is 1) 2 2) 1 3) 4 4) 3 Key-4

150. Which of the following are the correct representations of a zero order reaction, where A represents the reactant ?

[A]012

t12k

[A]0 [A]

Rate

[A]

Rate

(a) (b) (c) (d) 1) a, b, c 2) a, b, d 3) b, c, d 4) a, c, d Key-2 151. Which of the following is true for spontaneous adsorption of H2 gas without dissociation on solid surface 1) Process is exothermic and S 0 2) Process is endothermic and S 0 3) Process is exothermic and S 0 4) Process is endothermic and S 0 Key-1 152. Reaction of calgon with hard water containing 2Ca ions produce 1) 2

2 6 18Na CaP O 2) 2 4 3Ca PO 3) 3CaCO 4) 4CaSO

Key-1 153. Nitration of phenyl benzoate yields the product

O

O

NO2

O

ONO2

O

O

NO2

O

O

O N2

(1) (2)

(3) (4)

Key-2 154. Commercially available 2 4H SO is 98gms by weight of 2 4H SO and 2gms by weight of water. It’s density

is 1.83 g cm-3. Calculate the molality (m) of 2 4H SO (molar mass of 2 4H SO is 98 g mol-1) 1) 500 m 2) 20 molal 3) 50 m 4) 200 m Key-1 155. The set representing the right order of ionic radius is 1) 2 2Li Na Mg Be 2) 2 2Mg Be Li Na 3) 2 2Na Mg Li Be 4) 2 2Na Li Mg Be Key-3 156. Cyclohexylamine and aniline can be distinguished by 1) Hinsberg test 2) Carbylamine test 3) Lassaigne test 4) Azo dye test Key-4 157. The species having pyramidal shape according VSEPR theory is

1) 3SO 2) 3BrF 3) 23SiO 4) 2SoF

Key-0 158. The reactivity of alkyl bromides

a) 3 2CH CH Br b) 3

3

CH CH Br | CH

C)

3

3

3

CH |CH C Br | CH

d) 3CH Br

Towards iodide ion in dry acetone decreases the order. 1) D > A > B > C 2) A > D > B > C 3) C > B > A > D 4) C > B > D > A Key-1 159. Which one of the following statement is correct for d4 ions [P = pairing energy] 1) When 0 P, low-spin complex form 2) When 0 P, low-spin complex form 3) When 0 P, high-spin complex form 4) When 0 P, both high-spin and low-spin complexes form Key-1 160. Which among the following is the strongest acid ? 1) HF 2) HCl 3) HBr 4) HI Key-4