eamcet 2013 engineering solutions engineering key with solutions

Engineering EAMCET-2013 Date: 10.05.13

Sri Chaitanya Page1 Hyderabad

SRI CHAITANYA EDUCATIONAL INSTITUTIONS, A.P. HYDERABAD Guntur VIJAYAWADA Visakhapatnam Tirupathi Eluru Bhimavaram Rajahmundry Kakinada Machilipatnam Tenali Srikakulam Ongole Anantapuram Nellore Amalapuram Chittoor Kurnool

CENTRAL OFFICE- MADHAPUR

EAMCET -2013 (CODE-B) DATE : 10-

05-13

MATHS

1. If the equation 2 22 2 2 0ax hxy by gx fy c+ + ++ + + = represents a pair of straight lines, then

the square of the distance of their point of intersection from the origin is

1) ( ) 2 2

2

+ - -

-

c a b af bg

ab h 2)

( ) 2 2

2

+ + +

-

c a b f g

ab h

3) ( ) 2 2

2

+ - -

-

c a b f g

ab h 4)

( )

( )

2 2

22

+ - -

-

c a b f g

ab h

ANS : 3

2. The equation 2 25 3 8 2 0- + + - + =x xy py x y represents a pair of straight lines. If q is

the angle between them, then sinq=

1) 1

50 2)

17

3) 15

4) 1

10

ANS : 1

3. The equation of the pair of lines passing through the origin whose sum and product of

slopes are respectively the arithmetic mean and geometric mean of 4 and 9 is

1) 2 212 13 2 0- + =x xy y 2) 2 212 13 2 0+ + =x xy y

3) 2 212 15 2 0- + =x xy y 4) 2 212 15 2 0+ - =x xy y

ANS : 1

4. If the points (1, 2) and (3, 4) lie on the same side of the straight line 3 5 0- + =x y a

then a lies in the set

1) [7, 11] 2) [7, 11]-R 3) [7, ) 4) ( , 11]

ANS : 2



5. If 2 3 5+ =x y is the perpendicular bisector of the line segment joining the points

11,

3A and B, then B =

1) 21 49,

13 39 2) 17 31

,13 39

3) 7 49,

13 39 4) 21 31

,13 39

ANS : 1

6. If p and q are the perpendicular distances from the origin to the straight lines

sec cosq q- =x y ec a and cos sin cos2q q q+ =x y a , then

1) 2 2 24 + =p q a 2) 2 2 2+ =p q a 3) 2 2 22+ =p q a 4) 2 2 24 2+ =p q a

ANS : 1

7. The origin is translated to (1, 2). The point (7, 5) in the old system undergoes the

following transformations successively.

i) Moves to the new point under the given translation of origin

ii) Translated through 2 units along the negative direction of the new X-axis

iii) Rotated through an angle 4p

about the origin of new system in the clockwise

direction.

The final position of the point (7, 5) is

1) 9 1,

2 2

- 2) 7 1,

2 2 3) 7 1

,2 2

- 4) 5 1,

2 2

-

ANS : 3 8. If X is a Poisson variate and ( ) ( )1 2 2= = =P X P X then ( )3= =P X

1) 1

6

-e 2)

2

2

-e 3)

1

2

-e 4)

1

3

-e

ANS : 1

9. The random variable takes the values 1, 2, 3, , m. If ( ) 1= =P X n

m to each n, then

the variance of X is

1) ( )( )1 2 1

6

+ +m m 2)

2 112

-m 3)

12+m

4) 2 112

+m

ANS : 2



10. A bag contains 2 1+n coins. It is known that n of these coins have a head on both sides,

whereas the remaining 1+n coins are fair. A coin is picked up at random from the

bag and tossed. If the probability that the toss results in a head is 3142

, then n =

1) 10 2) 11 3) 12 4) 13

ANS : 1

11. Two fair dice are rolled. The probability of the sum of digits on their faces to be

greater than or equal to 10 is

1) 15

2) 14

3) 18

4) 16

ANS : 4

12. Two numbers are chosen at random from {1, 2, 3, 4, 5, 6, 7, 8} at a time. The

probability that smaller of the two numbers is less than 4 is

1) 7

14 2)

814

3) 9

14 4)

1014

ANS : 3 13. If

ra and

rb are two non-zero perpendicular vectors, then a vector

ury satisfying

equations r ura y c (c scalar) and

r ur ra y b is

1) ( )( )2r r r ra ca a b 2) ( )( )2r r r r

a ca a b 3) ( )( )2

1 r r rr ca a ba

4) ( )( )2

1 r r rr ca a ba

ANS : 3

14. A unit vector coplanar with 3+ +r r ri j k and 3+ +

r r ri j k and perpendicular to + +

r r ri j k is

1) ( )1

2+j k 2) ( )1

3- +

r r ri j k 3) ( )1

2-

r rj k 4) ( )1

3+ -

r r ri j k

ANS : 3

15. The shortest distance between the lines ( )3 5 7 2l= + + + + +r r r r r r rr i j k i j k and

( )7 6m= - - + + - +r r r r r r rr i j k i j k is

1) 16

5 5 2)

26

5 5 3)

36

5 5 4)

46

5 5

ANS : 4 16. 0, 0, 0, 0, 0

r r r r r r r r r r r r ra b c a b b c a c

1) rb 2)

ra 3) 0

r 4) + +

r r ri j k

ANS : 3



17. P, Q, R and S are four points with the position vectors 3 4 5- +r r ri j k , 4

rk , 4 5- + +

r r ri j k

and 3 4 3- + +r r ri j k respectively. Then the line PQ meets the line RS at the point.

1) 3 4 3+ +r r ri j k 2) 3 4 3- + +

r r ri j k 3) 4- + +

r r ri j k 4) + +

r r ri j k

ANS : 2

18. The points whose position vectors are 2 3 4+ +r r ri j k , 3 4 2+ +

r r ri j k and 4 2 3+ +

r r ri j k are the

vertices of

1) an isosceles triangle 2) right angled triangle

3) equilateral triangle 4) right angled isosceles triangle

ANS : 3

19. A person observes the top of a tower from a point A on the ground. The elevation of

the tower from this point is 60o . He moves 60 m in the direction perpendicular to the

line joining A and base of the tower. The angle of elevation of the tower from this

point is 45o . Then the height of the tower (in meters) is

1) 3

602

2) 60 2 3) 60 3 4) 2

603

ANS : 1

20. If, in DABC , 1 1 3

,a c b c a b c

=+ + + +

then the angle C =

1) 030 2) 045 3) 060 4) 090

ANS : 3

21. In any triangle ABC, 1 2 2 3 3 1+ + =rr r r r r

1) 2

2

Dr

2) Dr

3) 2Dr

4) 2D

ANS : 1

22. ( )1 11tan cot 2

2- -+ =h h

1) 1

log32

2) 1

log 62

3) 1

log122

4) log3

ANS : 4

23. 1 1 15 3cos cos cos

13 5- - - x x

1) 3

65 2)

3665

- 3)

3365

- 4) 1

ANS : 3



24. The set of solutions of the system of equations : 23p

+ =x y and 3cos cos

2+ =x y , where

x, y are real, is

1) ( ) 1, : cos

2 2-

=x y

x y 2) ( ) 1, : sin

2 2-

=x y

x y

3) ( ) ( ) 1, : cos

2- =x y x y 4) empty set

ANS : 4

25. If tan ( ) ( )cos cot sinp q p q= then a value of cos4p

q - among the following is

1) 1

2 2 2) 1

2 3)

12

4) 14

ANS : 1

26. sin cosq q+ = p , 3 3sin cosq q+ = q ( )2 3p p

1) q 2) 2q 3) q 4) 2q

ANS : 4

27. The period of ( ) cos sin3 2

= +x x

f x is

1) 2p 2) 4p 3) 8p 4) 12p

ANS : 4

28. ( ) ( )

( )1 1 2

1 ,2 2

+ - + +

+ -

i x i i y ix y

i i

1) 7 7

,3 15

- 2)

7 7,

3 15 3)

7 7,

5 15-

4) 7 7

,5 15

ANS : 1

29. If ( )1/( ) , 0= - >

nnf x p x p and n is a positive integer, then ( )( )=f f x

1) x 2) nx 3) 1/np 4) - np x

ANS : 1

30. ( ) ( ) ( ){ }2 6 1log 1.6 0.625

1- +x xx R R

1) ( , 1) (7, ) 2) ( 1, 5)- 3) (1, 7) 4) ( 1, 7)-

ANS : 4



31. If I is the identity matrix of order 2 and 1 1

0 1=A , then for 1n , mathematical

induction gives

1) ( )1= - -nA nA n I 2) ( )1= + -nA nA n I

3) ( )2 1= - +n nA A n I 4) ( )12 1-= - -n nA A n I

ANS : 1

32. 1 1330, 462, 462- +n n n

r r rC C C r

1) 3 2) 4 3) 5 4) 6

ANS : 3

33. 10 men and 6 women are to be seated in a row so that no two women sit together. The

number of ways they can be seated is :

1) 11! 10! 2) 11!6! 5!

3) 10! 9!

5! 4)

11! 10!5!

ANS : 4

34. If nt denotes the number of triangles formed with n points in a plane no three of which

are collinear and if 1 36+ - =n nt t , then n =

1) 7 2) 8 3) 9 4) 10

ANS : 3

35. The term independent of ( )0, 1x x x in the expansion of ( )

( )( )

( )

10

2/ 3 1/3

1 1

1

+ --

- + -

x x

x x x xis

1) 105 2) 210 3) 315 4) 420

ANS : 2

36. If x is small so that 2x and higher powers can be neglected, then the approximate

value for ( ) ( )

( )

1 2

3

1 2 1 3

1 4

- -

-

- -

-

x x

x is

1) 1 2- x 2) 1 3- x 3) 1 4- x 4) 1 5- x

ANS : 3

37. If 4 2 2 2

11 1 1

+ += +

+ + + + - +Ax B Cx D

x x x x x x, then C + D =

1) 1 2) 1 3) 2 4) 0



ANS : 4

38. 1 1 1 1........

2.3 4.5 6.7 8.9+ + + +

1) 2log

e 2) log

2e 3) ( )log 2e 4) 1-e

ANS : 2

39. If the harmonic mean between the roots ( ) ( )25 2 8 2 5 0+ - + + =x bx is 4, then the

value of b

1) 2 2) 3 3) 4 5- 4) 4 5+

ANS : 4

40. The set of solutions satisfying both 2 5 6 0x x and 2 3 4 0+ - <x x is

1) ( )4, 1- 2) ( ] [ )4, 3 2, 1 3) ( ) ( )4, 3 2, 1 4) [ ] [ ]4, 3 2, 1

ANS : 2

41. If the roots of 3 242 336 512 0- + - =x x x , are in increasing geometric progression, then

its common ratio is

1) 2 2) 3 3) 4 4) 6

ANS : 3

42. If a and b are the roots of the equation 2 2 4 0- + =x x , then 9 9a b+ =

1) 82- 2) 92 3) 102- 4) 102

ANS : 3

43. If 8 5

2 4

-=A satisfies the equation 2 4 0+ - =x x p , then p =

1) 64 2) 42 3) 36 4) 24

ANS : 2

44. 2 3 5

4 6 9

8 11 15

x x x

x x x

x x x

1) 23 4 5x x 2) 3 8 2x x 3) 0 4) 2

ANS : 4

45. The system of equations 3 2 6,3 4 3 14,x y z x y z 6 10 8 ,x y z a has infinite

number of solutions, if a =

1) 8 2)12 3) 24 4) 36



ANS : 4

46. The number of real values of t such that the system of homogeneous equations

( 1) ( 1) 0tx t y t z

( 1) ( 2) 0t x ty t z

( 1) ( 2) 0t x t y tz

has non-trivial solutions, is

1) 3 2) 2 3) 1 4) 4

ANS : 3

47. 4 4

1 11 1

i ii i

1) 0 2) 1 3) 2 4) 4

ANS : 3

48. If a complex number z satisfies 22 1 1,z z then z lies on :

1) the real axis 2) the imaginary axis 3) y=x 4) a circle

ANS : 2

49. The solution of the differential equation 2 tan 2 sec2xdyy x e x

dx is :

1) sin2 xy x e c 2) cos2 xy x e c

3) cos2xy e x c 4) cos2 xy x e c

ANS : 2

50. An integrating factor of the equation 2 3(1 ) ( ) 0y x y dx x x dy is

1) xe 2) 2x 3) 1x

4) x

ANS : 4

51. The approximate value of 3

1 2 3dx

x 1,3

into two equal parts is

1) 1 11log

3 5 2)

107110

3) 29

110 4)

119440

ANS : 3

52. The area (in square units) bounded by the curves 22x y and 21 3x y is



1) 23

2) 1 3) 43

4) 53

ANS : 3

53. If 2 2

0

,1 1

b

b

dx dxx x

then b =

1) 1 1tan

3 2) 3

2 3) 2 4) 1

ANS : 4

54. (log 2)(log 3)

dxI c I

x x x- -

1) 1 log 3

loglog 2

xx x

2) log 3

loglog 2

xx

3) log 2

loglog 3

xx

4) log (log 3)(log 2)x x

ANS : 2

55. sin

tan log sec1 cos 2 2x x x x

dx x p c px

1) -4 2) 4 3) 2 4) -2

ANS : 1

56. 2 sin 21 cos2

x xe dx

x

1) cotxe x c 2) 22 secxe x c 3) cos2xe x c 4) tanxe x c

ANS : 4

57. 3 3 3log( 3 )u x y z xyz ( )( )x y zx y z u u u

1) 0 2) x y z 3) 2 4) 3

ANS : 4

58. The focal length of a mirror is given by 2 1 1

.f v u

In finding the values of u and v,

in f is

1) 1 1

2p

u v 2)

1 1p

u v 3)

1 12p

u v 4)

1 1p

u v

ANS : 2

59. If the curves 2 2 1x py and 2 2 1qx y are orthogonal to each other, then

1) 2p q 2) 1 1

2p q

3) 1 1

2p q

4) 1 1

2p q



ANS : 4

60. The relation between pressure p and volume v is given by 14pv Constant. If the

percentage decrease in volume is 12

, then the percentage increase in pressure is

1) 18

2) 1

16 3)

18

4) 12

ANS : 3

61. 1cos 2log , 02

y xx

b

22

2

d y dyx x

dx dx=

1) 4y 2) -4y 3) 0 4) -8y

ANS : 2

62. 2 4 8( 1)( 1)( 1)( 1)d

x x x xdx

2(15 16 1)( 1)p qx x x ( , )p q

1) (12,11) 2) (15,14) 3) (16,14) 4) (16,15)

ANS : 4

63. 2y x dyx y dx

1) 2 2x yx y

2) 2 2x yx y

3) 1 4) 2

ANS : 3

64. 1

( ) ; ( )1

1f x g x

x

'1(2)

11

( )

g

f x

1) 15

2) 125

3) 5 4) 1

16

ANS : 2

65. 3 3

50

tan sinlimx

x xx

1) 52

2) 32

3) 35

4) 25

ANS : 2

66. Let f be a non-zero real valued continuous function satisfying ( ) ( ). ( )f x y f x f y for

all x, . (2) 9,y R If f then (6)f

1) 23 2) 63 3) 43 4) 33



ANS : 2

67. A variable plane passes through a fixed point (1,2,3). Then the foot of the

perpendicular form the origin to the plane lies on

1) a circle 2) a sphere 3) an ellipse 4) a parabola

ANS : 2

68. A plane passing through (-1,2,3) and whose normal makes equal angles with the

coordinate axes is

1) 4 0x y z 2) 4 0x y z 3) 4 0x y z 4) 0x y z

ANS : 3

69. The direction ratios of two lines AB,AC are 1, 1, 1 and 2, 1,1. The direction ratios of

the normal to the plane ABC are

1) 2,3, 1 2) 2,2,1 3) 3,2, 1 4) 1,2,3

ANS : 1

70. (2,1,0), (2,0,0), (0,1,0)D E F are mid-points of the sides , ,BC CA AB OF ABC respectively

Then, the centroid of ABC is

1) 1 1 1

, ,3 3 3

2) 4 2, ,0

3 3 3) 1 1 1

, ,3 3 3

4) 2 1 1, ,

3 3 3

ANS : 2

71. The perpendicular distance from the point (1, ) to the line joining 0(1,0 ) and (1, ),2

(in

polar coordinates ) is

1) 2 2) 3 3) 1 4) 2

ANS : 4

72. If 9x is a chord of contact of the hyperbola 2 2 9,x y then the equation of the

tangent at one of the points of contact is

1) 3 2 0x y+ + = 2) 3 2 2 3 0x y- - = 3) 3 2 6 0x y- + = 4) 3 2 0x y- + =

ANS : 2

73. If the foci of the ellipse 2 2

125 16x y

and the hyperbola 2 2

21

4x y

b coincide, then 2b

1) 4 2) 5 3) 8 4) 9

ANS : 2



74. The midpoint of a chord of the ellipse 2 24 2 20 0x y x y is (2, -4). The equation of

the chord is

1) 6 26x y 2) 6 26x y 3) 6 26x y 4) 6 26x y

ANS : 1

75. A circle of radius 4, drawn on a chord of the parabola 2 8y x as diameter, touches the

axis of the parabola, Then, the slope of the chord is

1) 12

2) 34

3) 1 4) 2

ANS : 3

76. If the circle 2 2 4 6 0x y x y c bisects the circumference of the circle

2 2 6 4 12 0,x y x y then c

1) 16 2) 24 3) -42 4) -62

ANS : 4

77. (a,0) and (b,0) are centres of two circles belonging to a co-axial system of which y-axis

is the rad

circle is

1) 2 2 2 1/2( )r b a 2) 2 2 2 1/2( )r b a 3) 2 2 2 1/3( )r b a 4) 2 2 2 1/3( )r b a

ANS : 2

78. If the length of the tangent from (h, k) to the circle 2 2 16x y is twice the length of

the tangent from the same point to the circle 2 2 2 2 0,x y x y then

1) 2 2 4 4 16 0h k h k 2) 2 2 3 3 0h k h k

3) 2 23 3 8 8 16 0h k h k 4) 2 23 3 4 4 16 0h k h k

ANS : 3



79. For the circle C with the equation 2 2 16 12 64 0x y x y match the list-I with the

list-II given below.

List-I List-II

i) The equation of the polar of (-5,1) with respect to C a) 0y

ii) The equation of the tangent at (8, 0) to C b) y=6

iii) The equation of the normal at (2, 6) to C c) 7x y

iv) The equation of the diameter of C through (8, 12) d) 13 5 98x y

e) 8x

Correct match is

i ii iii iv i ii iii iv

1) d b a e 2) d a b e

3) c d a b 4) c e b a

ANS : 2

80. The circle 2 24 4 12 12 9 0x y x y

1) touches both the axes 2) touches the x-axis only

3) touches the y-axis only 4) does not touch the axes

ANS : 1

PHYSICS

81. A tension of 20N applied to a copper wire of cross sectional area 0.01cm2, Young s

Modulus of copper is 11 21.1 10 /N m and Poisson s ratio is 0.32. The decrease in cross

sectional area of the wire is

1) 6 21.16 10 cm- 2) 5 21.16 10 m- 3) 4 21.16 10 m- 4) 3 21.16 10 cm-

ANS : 1

82. A capillary tube of radius r is immersed in water and water rises to a height of h .

Mass of water in the capillary tube is 35 10 kg- . The same capillary tube is now

immersed in a liquid whose surface tension is 2 times the surface tension of water.

The angle of contact between the capillary tube and this liquid is 450. The mass of liquid

which rises into the capillary tube now is, (in kg)

1) 35 10- 2) 32.5 10- 3) 35 2 10- 4) 33.5 10-



ANS : 1

83. The terminal velocity of a liquid drop of radius r falling through air is v. If two such

drops are combined to form a bigger drop, the terminal velocity with which the bigger

drop falls through air is (Ignore any buoyant force due to air)

1) 2v 2) 2 v 3) 3 4v 4) 3 2v

ANS : 3

84. A glass flask of volume one litre is filled completely with mercury at 00C. The flask is

now heated to 1000C. Coefficient of volume expansion of mercury is 4 01.82 10 / C- and

coefficient of linear expansion of glass is 4 00.1 10 / C- . During this process, amount of

mercury which overflows is

1) 21.2 cc 2) 15.2 cc 3) 2.12 cc 4) 18.2 cc

ANS : 2

85. On a temperature scale Y, water freezes at -1600 Y and boils at -500 Y. On this Y scale,

a temperature of 340 K is

1) 0106.3 Y- 2) 096.3 Y- 3) 086.3 Y- 4) 076.3 Y-

ANS : 3

86. Three moles of an ideal monoatomic gas undergoes a cyclic process as shown in the

figure. The temperature of the gas in different states marked as 1,2,3 and 4 are 400 K,

700 K, 2500 K and 1100 K respectively. The work done by the gas during the process 1-

2-3-4-1 is (Universal gas constant R)

1) 1650 R 2) 550 R 3) 1100 R 4) 2200 R

ANS : 1

87. Efficiency of a heat engine whose sink is at a temperature of 300 K is 40%. To increase

the efficiency to 60%, keeping the sink temperature constant, the source temperature

must be increased by



1) 750 K 2) 500 K 3) 250 K 4) 1000 K

ANS : 3

88. Two bodies A and B of equal surface area have thermal emissivities of 0.01 and 0.81

respectively. The two bodies are radiating energy at the same rate. Maximum energy is

radiated from the two bodies A and B at wavelengths Al and Bl respectively.

Difference in these two wavelengths is 1 mm . If the temperature of the body A is 5802 K,

then value of Bl is

1) 12

mm 2) 1 mm 3) 2 mm 4) 32

mm

ANS : 4

89. An air column in a tube 32 cm long, closed at one end, is in resonance with a tuning

fork. The air column in another tube, open at both ends, of length 66 cm is in resonance

with another tuning fork. When these two tuning forks are sounded together, they

produce 8 beats per second. Then the frequencies of the two tuning forks are, (Consider

fundamental frequencies only)

1) 250 Hz, 258 Hz 2) 240 Hz, 248 Hz 3) 264 Hz, 256 Hz 4) 280 Hz, 272 Hz

ANS : 3

90. A source of sound of frequency 640 Hz is moving at a velocity of 100

3m/s along a road,

and is it an instant 30 m away from a point A on the road (as shown in figure). A person

standing at O, 40 m away from the road hears sound of apparent frequency v1. The

value of v1 is (velocity of sound = 340 m/s)

1) 620 Hz 2) 680 Hz 3) 720 Hz 4) 840 Hz

ANS : 2



91. The two surfaces of a concave lens, made of glass of refractive index 1.5 have the same

radii of curvature R. It is now immersed in a medium of refractive index 1.75, then the

lens

1) becomes a convergent lens of focal length 3.5 R

2) becomes a convergent lens of focal length 3.0 R

3) changes as a divergent lens of focal length 3.5 R

4) changes as a divergent lens of focal length 3.0 R

ANS : 1

92. A microscope consists of an objective of focal length 1.9 cm and eye piece of focal length

5 cm. The two lenses are kept at a distance of 10.5 cm. If the image is to be formed at

the least distance of distinct vision, the distance at which the object is to be placed

before the objective is (Least distance of distinct vision is 25 cm)

1) 6.2 cm 2) 2.7 cm 3) 21.0 cm 4) 4.17 cm

ANS : 2

93. Fresnel diffraction is produced due to light rays falling on a small obstacle. The

intensity of light at a point on a screen beyond an obstacle depends on

1) the focal length of lens used for observation

2) the number of half-period zones that superpose at the point

3) the square of the sum of the number of half period zones

4) the thickness of the obstacle

ANS : 2

94. A short bar magnet having magnetic moment 4 Am2, placed in a vibrating

magnetometer, vibrates with a time period of 8 seconds. Another short bar magnet

having a magnetic moment 8 Am2 vibrates with a time period of 6 seconds. If the

moment of inertia of the second magnet is 2 29 10 kg m- , the moment of inertia of the

first magnet is

(Assume that both magnets are kept in the same uniform magnetic induction field.)

1) 2 29 10 kg m- 2) 2 28 10 kg m- 3) 2 25.33 10 kg m- 4) 2 212.2 10 kg m-

ANS : 2



95. Two short bar magnets have their magnetic moments 1.2 Am2 and 1.0 Am2. They are

placed on a horizontal table parallel to each other at a distance of 20 cm between their

centres, such that their north poles pointing towards geographic south. They have

common magnetic equatorial line. Horizontal component of earth s field is 53.6 10 T- .

Then, the resultant horizontal magnetic induction at mid point of the line joining their

centers is 70 10 H / m4

-m=

p

1) 53.6 10 T- 2) 41.84 10 T- 3) 42.56 10 T- 4) 55.8 10 T-

ANS : 3

96. A deflection magnetometer is adjusted and a magnet of magnetic moment M is placed

on it in the usual manner and the observed deflection is q . The period of oscillation of

the needle before settling to the deflection is T. When the magnet is removed, the period

of oscillation of the needle is 0T before settling to 0 00 0- . If the earth s induced magnetic

field is HB , the relation between

T and T0 is

1) 2 20T T cos= q 2)

22 0T

Tcos

=q

3) 0T T cos= q 4) 0TT

cos=

q

ANS : 1

97. Two metal plates each of area A form a parallel plate capacitor with air in between

the plates. The distance between the plates is d . A metal plate of thickness d/2 and of

same area A is inserted between the plates to form two capacitors of capacitances C1

and C2 as shown in the figure. If the effective capacitance of the two capacitors is |C and

the capacitance of the capacitor initially is C, then C 'C

is

1) 4 2) 2 3) 6 4) 1

ANS : 2



98. In the circuit shown in the figure, the current I is

1) 6 Amp 2) 2 Amp 3) 4 Amp 4) 7 Amp

ANS : 3

99. In the meter bridge experiment, the length AB of the wire is 1m. The resistors X and Y

have values 5 W and 2 Wrespectively. When a shunt resistance S is connected to X, the

balancing point is found to be 0.625 m from A. Then, the resistance of the shunt is

1) 5W 2) 10W 3) 7.5W 4) 12.5W

ANS : 2

100. If E,M,J and G respectively denote energy, mass, angular momentum and universal

gravitational constant, the quantity, which has the same dimensions as the dimensions

of 2

5 2

EJM G

1) Time 2) Angle 3) Mass 4) Length

ANS : 2

101. The work done in moving an object from origin to a point whose position vector is

r 3i 2j 5k= + - by a force F 2i j k= - - is

1) 1 unit 2) 9 units 3) 13 units 4) 60 units

ANS : 2



102. A particle is projected from the ground with an initial speed of v at an angle of

projection q . The average velocity of the particle between its time of projection and

time it reaches highest point of trajectory is

1) 2v1 2cos

2+ q 2) 2v

1 2sin2

+ q 3) 2v1 3cos

2+ q 4) vcos q

ANS : 3

103. Two wooden blocks of masses M and m are placed on a smooth horizontal surface as

shown in figure. If a force P is applied to the system as shown in figure such that the

mass m remains stationary with respect to block of mass M, then the magnitude of the

force P is

1) ( )M m g tan+ b 2) g tanb 3) mgcosb 4) ( )M m gcosec+ b

ANS : 1

104. A ball at rest is dropped from a height of 12m. It looses 25% of its kinetic energy on

striking the ground and bounces back to a height h . Then value of h is

1) 3 m 2) 6 m 3) 9 m 4) 12 m

ANS : 3

105. Two bodies of mass 4kg and 5 kg are moving along east and north directions with

velocities 5 m/s and 3m/s respectively. Magnitude of the velocity of centre of mass of the

system is

1) 25

m / s9

2) 9

m / s25

3) 41

m / s9

4) 16

m / s9

ANS : 1

106. A mass of 2.9 kg is suspended from a string of length 50 cm and is at rest. Another body of mass 100 g, which is moving horizontally with a velocity of 150 m/s strikes and sticks to it. Subsequently when the string makes an angle of 060 with the vertical, the tension in the string is ( )2g 10m / s=

1) 140 N 2) 135 N 3) 125 N 4) 90 N ANS : 2



107. The upper half of an inclined plane with an angle of inclination f , is smooth while the

lower half is rough. A body starting from rest at the top of the inclined plane comes to

rest at the bottom of the inclined plane. Then the coefficient of friction for the lower

half is

1) 2tan f 2) tan f 3) 2sin f 4) 2cosf

ANS : 1

108. Moment of inertia of a body about an axis is 24kgm . The body is initially at rest and a

torque of 8 Nm starts acting on it along the same axis. Work done by the torque in 20

sec, in Jules, is

1) 40 2) 640 3) 2560 4) 3200

ANS : 4

109. A uniform circular disc of radius R, lying on a frictionless horizontal plane is rotating

with an angular velocity w about its own axis. Another identical circular disc is gently

placed on the top of the first disc coaxially. The loss in rotational kinetic energy due to

friction between the two discs, as they acquire common angular velocity is (I is Moment

of Inertia of the disc)

1) 21I

8w 2) 21

I4

w 3) 21I

2w 4) 2Iw

ANS : 2

110. The gravitational force acting on a particle, due to a solid sphere of uniform density and

radius R, at a distance of 3R from the centre of the sphere is 1F . A spherical hole of

radius (R/2) is now made in the sphere as shown in the figure. The sphere with hole now

exerts a force 2F on the same particle. Ratio of 1F to 2F is

1) 5041

2) 4150

3) 4125

4) 2541

ANS : 1



111. Two particles A and B of masses m and 2m are suspended from two massless springs

of force constants 1K and 2K . During their oscillation, if their maximum velocities are

equal, then ratio of amplitudes of A and B is

1) 1

2

KK

2) 2

1

K2K

3) 2

1

KK

4) 1

2

2KK

ANS : 2

112. Of the following, NAND gate is

1) 2)

3) 4)

ANS : 4

113. The base current in a transistor circuit changes from 45 mA to 140 mA. Accordingly, the

collector current changes form 0.2 mA to 4.00 mA. The gain in current is

1) 9.5 2) 1 3) 40 4) 20

ANS : 3

114. A 235U nuclear reactor generates energy at rate of 73.70 10 J / s . Each fission liberates

185 MeV useful energy. If the reactor has to operate for 4144 10 seconds, then, the

mass of the fuel needed is (Assume Avogadro s number = 23 1 196 10 mol ,1eV 1.6 10 J- - )

1) 70.5 kg 2) 0.705 kg 3) 13.1 kg 4) 1.31 kg

ANS : 2

115. The radius of 12572Te nucleus is 6 fermi. The radius of 27

13 A1 nucleus in meters is 12572Te

1) 123.6 10 m- 2) 153.6 10 m- 3) 87.2 10 m- 4) 157.2 10 m-

ANS : 2

116. The work function of a metal is 2 eV. If a radiation of wavelength 3000 0A is incident on

it, the maximum kinetic energy of the emitted photoelectrons is

(Planack s constant 34h 6.6 10 JS;- Velocity of light 8c 3 10 m / s; 191eV 1.6 10 J- )

1) 194.4 10 J- 2) 195.6 10 J- 3) 193.4 10 J- 4) 192.5 10 J-

ANS : 3



117. Initially a photon of wavelength 1l falls on photocathode and emits an electron of

maximum energy 1E . If the wavelength of the incident photon is changed to 2l , the

maximum energy of the electron emitted becomes 2E . Then value of hc (h = Planck s

constant, c = Velocity of light )is

1) ( )1 2 1 2

2 1

E Ehc

+ l l=

l - l 2) ( )1 2

1 22 1

E Ehc

-= l l

l - l

3) ( )( )1 2 2 1

1 2

E Ehc

- l - l=

l l 4) 2 1

11 2 2

hc .EE

l - l=

l l

ANS : 2

118. The sensitivity of a galvanometer that measures current is decreased by 140

times by

using shunt resistance of 10W. Then, the value of the resistance of the galvanometer is

1) 400W 2) 410W 3) 30W 4) 390W

ANS : 4

119. A series LCR circuit is connected across a source of alternating emf of changing

frequency and resonates at frequency 0f . Keeping capacitance constant, if the

inductance (L) is increased by 3 times and resistance is increased (R) by 1.4 times, the

resonant frequency now is

1) 1/403 f 2) 03 f 3) ( )

1/4

03 1 f- 4) 1/4

0

1f

3

ANS : 4

120. The ends of an element of zinc wire are kept at a small temperature difference TD and a

small current (I) is passed through the wire. Then, the heat developed per unit time

1) is proportional to TD and I 2) is proportional to 3I and TD

3) is proportional to Thomson coefficient of the metal 4) is proportional to TD only

ANS : 1



CHEMISTRY

121. For which one of the following reactions, the entropy change is positive ?

1) 2 2 2

12

( ) ( ) ( )

H O H O

g g l 2)

( ) ( ) ( )

Na Cl NaCl

g g s

+ -

3) ( ) ( )

NaCl NaCl

l s 4) 2 2

( ) ( )

H O H O

l g

ANS : 4

122. Match the following

List-I List-II

A) Solid dispersed in liquid I) Emulsion

B) Liquid dispersed in liquid II) Foam

C) Gas dispersed in liquid III) Gel

D) Liquid dispersed in solid IV) Sol

V) Aerosol

A B C D A B C D

1) IV I II III 2) III I V II

3) III I II IV 4) IV I V III

ANS : 1

123. Observe the following statements :

1. Heavy water is harmful for the growth of animals

2. Heavy water reacts with 4 3Al C and forms deuterated acetylene

3. 2 2.2BaCl D O is an example of interstitial deuterate

The correct statements are :

1) 1 & 3 2) 1 & 2 3) 1,2 & 3 4) 2 & 3

ANS : 1

124. 2 3 3.Na CO and NaHCO 20 ml of X when titrated using methyl

Orange indicator consumed 60 ml of 0.1 M HCl solution. In another experiment, 20

ml of X solution when titrated using phenolphthalein consumed 20 ml of 0.1 M HCl

solution. The concentrations 1( )in mol lit- of 2 3 3Na CO and NaHCO in X are respectively

1) 0.01, 0.02 2) 0.1, 0.1 3) 0.01, 0.01 4) 0.1, 0.01

ANS : 2



125. Diborane reacts with HCl in the presence of 3AlCl and liberates :

1) 2H 2) 2Cl 3) 3BCl 4) 2 3&Cl BCl

ANS : 1

126. How many corners of 4SiO unit are shared in the formation of three dimensional

silicates ?

1) 3 2) 2 3) 4 4) 1

ANS : 3

127. Which one of the following is not correct ?

1) Pyrophosphoric acid is a tetrabasic acid

2) Pyrophosphoric acid contains P-O-P linkage

3) Pyrophosphoric acid contains two P-H bonds

4) Orthophosphoric acid can be prepared by dissolving 4 10PO in water

ANS : 3

128. 2 2 3Na S O reacts with moist 2Cl to form 2 4,Na SO HCl and X. Which one of the following is X ?

1) 2H S 2) 2SO 3) 3SO 4) S

ANS : 4

129. The role of copper diaphragm in Whytlaw-

1) preventing the corrosion of electrolytic cell 2) preventing the mixing of 2 2H and F

3) as anode 4) as cathode

ANS : 2

130. Liquid X is used in Bubble chamber to detect neutral mesons and gamma photons.

Then, X =

1) He 2) Ne 3) Kr 4) Xe

ANS : 4

131. A compound absorbs light in the wavelength region 490-500 nm. Its complementary

Colour is :

1) Red 2) Blue 3) Orange 4) Blue-green

ANS : 1

132. Which of the following is not added during the extraction of silver by cyanide process?

1) NaCN 2) Air 3) Zn 4) 2 2 3Na S O

ANS : 4



133. Cataract and skin cancer are caused by

1) Depletion of Nitric oxide 2) Depletion of Ozone layer

3) Increase in Methane 4) Depletion of Nitrous oxide

ANS : 2

134. Which one of the following gives Prussion blue colour ?

1) ( )2 6Fe Fe CN 2) ( )4 6

Na Fe CN 3) ( )3 6 3Fe Fe CN 4) ( )4 6 3

Fe Fe CN

ANS : 4

135. 2 6 2 4 2450 CC H C H H

Above reaction is called as

1) Combustion 2) Rearrangement 3) Pyrolysis 4) Cleavage

ANS : 3

136. Assertion (A) : 2NH- group of aniline is ortho, para directing in electrophilic

substitutions.

Reason (R) : 2NH- group stabilises the arenium ion formed by the ortho, para attack of the

electrophile.

The correct answer is

1) Both (A) and (R) are correct,(R) is the correct explanation of (A).

2) Both (A ) and (R) are correct, (R) is not the correct explanation of (A).

3) (A) is correct, but (R) is not correct

4) (A) is not correct, but (R) is correct

ANS : 1

137. In which of the following properties, the two enantiomers of lactic acid differ from

each other ?

1) Sign of specific rotation 2) Density

3) Melting point 4) Refractive index

ANS : 1

138. Heating chloroform with aqueous sodium hydroxide solution forms :

1) Sodium acetate 2) Sodium oxalate

3) Sodium formate 4) Chloral

ANS : 3



139. The products formed in the reaction of phenol with 2Br dissolved in 2CS at 0°C are :

1) o-bromo. m-bromo and p-bromophenols

2) o- bromo and p- bromophenols

3) 2, 4, 6-tri bromo and 2, 3, 6-tri bromophenols

4) 2, 4-di bromo and 2, 6-di bromophenols

ANS : 2

140. The structure of PCC is :

1) 2)

3) 4)

ANS : 4

141. The apK values of four carboxylic acids are given below. Identify the weakest

carboxylic acid.

1) 4.89 2) 1.28 3) 4.76 4) 2.56

ANS : 1

142. Identify X and Y in the following reactions :

ANS : 3



143. Example of a biodegradable polymer pair is :

1) Nylon-6,6 and Terylene 2) PHBV and Dextron

3) Bakelite and PVC 4) PET and Polyethylene

ANS : 2

144. The number of hydrogen bonds between Guanine & Cytosine; and between Adenine

& Thymine in DNA is :

1) 1, 2 2) 3, 2 3) 3, 1 4) 2, 1

ANS : 2

145. Identify Phenacetin from the following :

ANS : 4

146. The number of radial nodes of 3s and 2p orbitals respectively are :

1) 0, 2 2) 2, 0 3) 1, 2 4) 2, 1

ANS : 2

147. The basis of quantum mechanical model of an atom is :

1) angular momentum of electron 2) quantum numbers

3) dual nature of electron 4) black body radiation

ANS : 3

148. The number of elements present in fourth period is :

1) 32 2) 8 3) 18 4) 2

ANS : 3



149. Identify the correct set :

Molecule hybridisation of central atom shape

1) 5PCl 3dsp square pyramidal

2) ( )4

2Ni CN

- 3sp tetrahedral

3) 6SF 3 2sp d octahedral

4) 3IF 3dsp pyramidal

ANS : 3

150. Which one of the following statements is correct ?

1) Hybrid orbitals do not form s bonds

2) Lateral overlap of p-orbitals or p- and d-orbitals produces p - bonds

3) The strength of bonds follows the order : p p s s p ps s p- - -< <

4) s-orbitals do not form s bonds

ANS : 2

151. Which one of the following is an example of disproportionation reaction ?

1) 23 ( ) 6 ( )Cl g OH aq 3 2( ) 5 ( ) 3 (1)ClO aq Cl aq H O

2) 2 ( ) ( ) 2 ( )Ag aq Ag s Ag aq

3) 4( ) ( )Zn s CuSO aq 4( ) ( )Cu s ZnSO aq

4) 3 22 ( ) 2 ( ) 3 ( )KClO s KCl s O g

ANS : 1

152. At T(k), the ratio of Kinetic energies of 4 g of ( )2 g

H and 8gof( )2 :g

O is

1) 1: 4 2) 4 :1 3) 2 :1 4) 8 :1

ANS : 4

153. Which one of the following is an isotonic pair of solutions?

1) 0.15 M NaCl and 0.1 M 2 4Na SO

2) 0.2 M Urea and 0.1 M Sugar

3) 0.1 M 2BaCl and 0.2 M Urea

4) 0.2 M 4MgSO and 0.1 M 4NH Cl

ANS : 1



154. The vapour pressure in mm of Hg, of an aqueous solution obtained by adding 18 g of

glucose ( )6 12 6C H O to 180 g of water at 100oC is :

1) 7.60 2) 76.0 3) 759 4) 752.4

ANS : 4

155. During the electrolysis of copper sulphate aqueous solution using copper electrode, the

reaction taking place at the cathode is :

1) ( )2 2aqCu Cu e+ - 2) ( ) ( )

2 2aq sCu e Cu+ -

3) ( ) ( )2

12aq gH e H+ - 4) ( ) ( ) ( )

24 23

12

2aq g gSO SO O e- -

ANS : 2

156. The extent of charge of lead accumulator is determined by

1) amount of 4PbSO in the battery 2) amount of 2PbO in the battery

3) specific gravity of 2 4H SO of the battery 4) amount of Pb in the battery

ANS : 3

157. The number of octahedral and tetrahedral holes respectively present in a hexagonal

close packed (hcp) crystal of X atoms are :

1) X, 2X 2) X, X 3) 2X, X 4) 2X, 2X

ANS : 1

158. Which one of the following plots is correct for a first order reaction?

ANS : 3



159. The degree of ionization of 0.10 M lactic acid is 4.0%

The value of cK is

1) 51.66 10- 2) 41.66 10- 3) 31.66 10- 4) 21.66 10-

ANS : 2

160. The pH of a buffer solution made by mixing 25 ml of 0.02 M 4NH OH and 25 ml of 0.2

M 4NH Cl at 25oC is : ( bpK of 4 4.8NH OH = )

1) 5.8 2) 8.2 3) 4.8 4) 3.8

ANS : 2

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