sri chaitanya educational institutions...t.s eamcet (engineering) code : a sri chaitanya jr college...

T.S EAMCET (Engineering) CODE : A Sri Chaitanya Jr College

Page No : 1

SRI CHAITANYA EDUCATIONAL INSTITUTIONS, INDIA. AP TELANGANA KARNATAKA TAMILNADU MAHARASHTRA DELHI RANCHI

TS EAMCET-2017 (Engineering) CODE- A

MATHEMATICS

1. If 0tan 20 , then

0 0

0 0

tan160 tan110

1 tan160 tan110

1) 21

2

2)

21

3)

21

4)

21

2

Sol: tan160 tan110

1 tan160 tan110

tan 20 cot 20

1 tan 20 cot 20

2

11

2 2

2. Consider the circle 2 2x y 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

Sol: C 3, 2 ,R 9 4 12 5

4x 3y k 0

12 6 k

d r 55

k 6 25 k 6 25

k 19,k 31

4x 3y 19 0,4x 3y 31 0


Page No : 2

3. 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

Sol: 6 7 10 12 13 12 16

108

76 2 80 4

4 3 0 2 3 6 2 6 26 13

M.D 3.258 8 4

4. Match the following.

List-I List-II

I)1

1x xdx

a) 2

II) 2

0

4 3sin x1 log dx

4 3cos x

b)

a

2

0f x dx

III) a

0f x dx c)

a

0f x f x dx

IV) a

af x dx

d) 0

e) a

0f a x dx

I II III IV

1) d a e c

2) d a c b

3) d c a e

4) a d b d


Page No : 3

Sol: 1) 1

1x xdx 0 odd

2) 2

0

4 3sin xF 1 log dx

4 3cos x

2

0

4 3cos x1 log dx

4 3sin x

2

02I 2dx I

2

5. 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) 3

11 2)

11

3 3) 8 4) 33

Sol: f x y f x f y

Diff w.r.t ‘x’ f ' x y f ' x f y

x 0,y 3 f ' 0 3 f ' 0 f 3 33

6. 2 20

xdx

4cos x 9sin x

1) 2

12

2)

2

4

3)

2

6

4)

2

3

Sol: 2 2

0

dxI

2 4cos x 9sin x

.2.2 2.3.2 12


Page No : 4

7. 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

The variance of X is

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

Sol: 0 0.4 0.6 0 1.6

2 0 0.4 1.2 1.8 2.56 0.84

8. If T

1 0 1

A 0 2 0 ,A B C,B B

1 1 4

and TC C , then C

1)

0 0.5 0

0.5 0 0

0 0 0

2)

0 0.5 0

0 0 0.5

0 0.5 0

3)

0 0.5 0.5

0.5 0 0

0.5 0 0

4)

0 0.5 0

0.5 0 0.5

0 0.5 0

Sol:

1 0 1 1 0 1 0 0 0

2C 0 2 0 0 2 1 0 0 1

1 1 4 1 0 4 0 1 0

0 0 0

C 0 0 0.5

0 0.5 0

9. If a is a unit vector, then 2 2 2

ˆ ˆ ˆa i a j a k

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

Sol: Put a i 2


Page No : 5

10. A bag contains 5 red balls, 3 black balls and 4 white balls are drawn at random. The

probability that they are not of same colour is

1) 37

44 2)

31

44 3)

21

44 4)

41

44

Sol: 5 3 4

3 3 3

12

3

C C C1

C

10 1 4 205 41

1220 220 41

11. The radical centre of the circles

2 2 2 2 2 2x y 4x 6y 5 0,x y 2x 4y 1 0,x y 6x 2y 0 lies on the line

1) x y 5 0 2) 2x 4y 7 0 3) 4x 6y 5 0 4) 18x 12y 1 0

Sol: R.A of (1) & (2) is 2x 2y 6 0 x y 3

R.A of (1) & (3) is 11 7

2x 4y 5 0 x 36 6

11

6y 11 y6

Radical centre 7 11

,6 6

12. If cosec cot 2017, then quadrant in which lies is

1) I 2) IV 3) III 4) II

Sol: 1

cosec cos2017

cosec cos 2017

12cosec 2017 ; sin ve

2017

12cot 2017; cot ve,cos ve

2017


Page No : 6

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

1) 2x1e f x g x C

2 2) 2x1

e f x g x C2

3) 2x1e f 2x g x C

2 4) 2x1

e f ' 2x g x C2

Sol: 2x 2xe f x dx e f x dx

2x 2x

2xe ef x f ' x dx e f ' x dx

2 2

2xe f x g x

c2 2

14. If A 5,3 ,B 3, 2 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

Sol: 5x 2y 19 18 a point of parallel lines

15. 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) 2x 3y 5 2) x y 2 3) x y 2 4) 2x y 5

Sol: b 2a equation of line 2x y b

Dist from b

0,0 1 b 5 2x y 55


Page No : 7

16. Let S and s ' be the foci of an ellipse and B be one end of its minor axis. If SBS’ is an

isosceles right angled triangle then the eccentricity of the ellipse is

1) 1

2 2)

1

2 3)

3

2 4)

1

3

Sol: 0 1e cos cos45

2

17. For the parabola 2y 6y 2x 5

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

Sol: 2

y 3 2x 5 9 Vertex 2, 3

2

y 3 2 x 2 Directrix 1

x 2 , 2x 5 02

18. If

2

22

x 5 A Bx C,

x 2 x 1x 1 x 2

then A B C

1) 1 2) 2

5 3)

3

5

4) 0

Sol: 2 2x 5 A x 1 Bx c x 2 9

x 2 9 5A A5

9 4

A B 1 B 15 5

9 8A 2C 5, 5 2C, C

5 5

9 4 8 3

A B C5 5 5 5


Page No : 8

19. If the conjugate of x iy 1 2i is 1 i , then

1) x iy 1 i 2) 1 i

x iy1 2i

3)

1 ix iy

1 2i

4)

1 ix iy

1 i

Sol: 3 1

x , y5 5

Then by verification 1 i

x iy1 2i

is true

20. 4 2xx e dx

1) 2x

4 3 2e2x 4x 6x 6x 3 C

4 2)

2x4 3 2e

2x 4x 6x 6x 3 C2

3) 2x

4 3 2e2x 4x 6x 6x 3 C

8 4)

2x4 3 2e

2x 4x 6x 6x 3 C4

Sol: 2x

4 2x 4 3 2ex e dx 2x 4x 6x 6x 3 c

4

21. 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

Sol: 0 0 0A 30 ,B 60 ,C 90

22. The sum of the complex roots of the equation 3

x 1 64 0 is

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

Sol: 3 3 2x 1 4 x 1 4 1, ,

2x 3 ,1 4 ,1 4

Sum of complex roots 3


Page No : 9

23. The area of the region bounded by the curves 2x y 2 and x y is

1) 9

4 2) 9 3)

9

2 4)

9

7

Sol: 2

2

1

y y 2 dx

23 2

1

y y 92y

3 2 2

24. If ˆ ˆ ˆa xi yj zk, then ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆˆ ˆ ˆa 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

Sol: a i yk zj a i . i j z

a j .k x a k . k i y

Value x y z

25. If the imaginary part of 2z 1

iz 1

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

Sol:

2 x iy 1 2x 1 2i y

i x iy 1 1 y ix

2 2

2x 1 2iy 1 y ix

1 y x

Im 2 2 2x 2x 1 1 y 2y 1 y x

2 2 2 22x x 2y 2y x y 1 2 it is straight line


Page No : 10

26. Let f : 1,1 R be a differentiable function with f 0 1 and f ' 0 1.

If 2

g x f 2f x 2 , then g ' 0

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

Sol: g' x 2f 2f x 2 2f ' x

g' 0 2 1 2 1 4

27. If the perpendicular distance between the point 1,1 to the line 3x 4y c 0 is 7, then

the possible values of c are

1) 35,42 2) 35,28 3) 42, 28 4) 28, 42

Sol: 7 c

75

7 c 35 7 c 35

7 c 35 c 42

c 28

28. The solution of dy x y

dx x y

is

1) 1 2 2ytan log x y C

x

2) 1 2 2y

tan log x y Cx

3) 1 2 2ysin log x y C

x

4) 1 2 2y

cos log x y Cx

Sol: xdv 1 v

vdx 1 v

xdv 1 v

vdx 1 v


Page No : 11

2xdv 1 v

dx 1 v

1 2

2

1 v dx 1dv tan v log 1 v log x c

1 v x 2

1 2 2y

tan log x y cx

29. If 2 2

2 2

x y1,

a b then

2

2

d y

dx

1) 4

2 3

b

a y

2)

2

2

b

ay 3)

3

2 3

b

a y

4)

3

2 2

b

a y

Sol: 2 2 2 2 2 2b x a y a b

2 2

12a yy 2b x

2

1yy b x

4 22 2

2 2

b xyy b x

y

30. 2 4y 1

1 2lim

y 1 y 1

1) 1

2 2)

1

3 3)

1

4 4) 0

Sol: 2 2 2y 1

1 2lim

y 1 y 1 y 1

2

4 3y 1 y 1

y 1 2 2y 1lim lim

y 1 4y 2


Page No : 12

31. The solution of 2y 3x dx xdy 0 is

1) 2

1y x sin x C

x 2) 2

1y x cos x C

x

3) 2 Cy x x

x 4)

Cy x x

x

Sol: 2y 3x dx xdy 0

2 dyy 3x x

dx

dy y

3xdx x

dy 1

y 3xdx x

I.F.

1dx

log xxe e x

3

2 xy.x 3x dx 3. c

3

32. If the coefficients of th

2r 1 term and th

r 1 term in the expansion of 42

1 x are equal

then r can be

1) 12 2) 14 3) 16 4) 20

Sol: 42 42

2r rC C

3r 42

r 14

33. 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


Page No : 13

Sol: a x 1 b y 1 c z 6 0 1

a 0 1 b 0 1 c 7 6 0 2 a b c 0

Perpendicular plane a 2b c 0 3 solving 2 & 3 we get a 2 c

3 2 1 3 2 2 7 0

3x 3 2y 2 z 6 0

3x 2y z 7 0

34. If the slope of the tangent to the curve 3y ax bx 4 at 2,14 is 21, then the values of a

and b are respectively

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

Sol: 8a 2 b 4 14 12a b 21

8a 2b 10 a 2,b 3

35. The probability distribution of a random variable X is given below.

x 1 2 3 4 5 6

P X x a a a b b 0.3

1) 0.3, 0.2 2) 0.1, 0.4 3) 0.1, 0.2 4) 0.2, 0.1

Sol: 3a 2b 0.7

a 2a 3a 4b 5b 1.8 4.2

6a 9b 2.4

a 0.1,b 0.2

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

1) 2

f 05

2)

2f 0

5

3)

3f 0

5

4)

3f 0

5


Page No : 14

Sol: 2f x ax bx c

4a 2b c 0 1 8a 4b 2c 0

c a b c 0 a b 2c 0 2

2a 2b 4c 0 7a 5b 0

6a 5c 0 7a

b5

5c 6a

a c6 5

2 7a 6a

ax x 05 5

25x 7x 6 0

2 3

5x 10x 3x 6 0 f 05

37. The equation of tangent to the curve

n nx y

2a b

at the point a,b is

1) x y

a b 2)

x y2

a b 3)

x y

a b 4)

x yn

a b

Sol: Given Curve 2

n nx y

a b

1 11 1

. . 0

n nx y dy

n na a b b dx

1 1n nn y dy n x

b b dx a a

11 nndy b x b

dx a a y


Page No : 15

,

1 1a b

b bm

a a

tann beq gent is y b x a

a

ay ab bx ab

2bx ay ab

2x y

a b

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

19 4 then k

1) 5

13 2)

13

5 3)

13

5 4)

5

13

Sol: The line 0lx my n is a normal to the hyperbola

2 2

2 21

x y

a b then

2

2 22 2

2 2 2

a ba b

l m n

Given hyperbola

2 2

19 4

x y

2 29, 4a b

Given line 0x y k

1, 1,l m n k

2

2

9 49 4

1 1 k

2

2

139 4

k

2 169

5k

13

5k


Page No : 16

39. The product of all the real roots of 2

2

8 1x 8x 9 0

x x is

1) 2 2) 1 3) 3 4) 7

Sol: Given equation 2

2

8 18 9 0x x

x x

2

2

1 18 9 0x x

x x

Put 1

x tx

S.B.S

2 2

2

12x t

x

2 2

2

12x t

x

2 2 8 9 0t t 2 8 7 0t t

2 7 7 0t t t 7 1 7 0t t t

7 1 0t t

1, 7t

17x

x

2 7 1 0x x

2 7 49 4

2x

7 45

2x

7 45 7 45

2 2

49 45 41

4 4


Page No : 17

40. If

1 5 6

0 1 7

0 0 1

and

1 0 1

' 3 0 3 ,

4 6 100

then

1) 2 13 0 2) 2

1 13 2 0

3) 2

1 13 5 0 4) 13 1 0

Sol: 11, 0

By verification

2 2 2

' 3 ' 2 1 0 3 1 0 2 1 3 2 0

41. 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) 10

6C 5! 4) 10

5C 6

Sol: 1st we select the 5 players from total 10 players in 10

5C ways and 6th

person will select from the

remaining 5 persons in 5 ways.

Total number of ways 10

5C 5 1260

42. 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


Page No : 18

Sol: Given lines 5x 6y 1 0 1

3x 2y 5 0 2

Solution (1) & (2) We get x,y 1, 1

The equation of required line is 5x 3y k 0 and it is passing through 1, 1 is

5 3 k 0

k 8

5x 3y 8 0

43. An integer is chosen form {2k / 9 k 10} . The probability that it is divisible by both 4

and 6 is

1) 1

10 2)

1

20 3)

1

4 4)

3

20

Sol: S { 18, 16, 14, ,20}

n S 20

E = Divisible by 4 and 6 i.e., integer is divisible by 12

{ 12,0,12}

n E 3

3

P E20


Page No : 19

44. 4

dx

x x 1

1) 4

4

1 x 1log C

4 x

2)

4

4

1 xlog C

4 x 1

3) 41log x 1 C

4 4)

4

4

1 xlog C

4 x 2

Sol:

3

4 4 4

1 1 4xdx dx

4x x 1 x x 1

put

4x t 34x dx dt

1 1 1 1 1dt dt

4 t t 1 4 t t 1

4

4

1 1 xlog t log t 1 c log c

4 4 d 1

45. 1 13 2sin sin

2 3

1) 1 3 2sin

2 3

2) 1 3 2

sin2 3

3) 1 3 2sin

2 3

4) 1 3 2sin

2 3

Sol: 1 13 2 3 2sin A; sin B sin ; sin B

2 3 2 3

2 23 2 3 2 17 1 1

x , y x y 1 cosA ;cosB2 3 4 3 12 2 3

, A B2

13 1 1 2 3 2 3 2sin A B . . A B sin

2 2 33 2 3 2 3


Page No : 20

1 1 13 2 3 2

sin sin sin2 3 2 3

46. and are the roots of 2x 2x C 0. If 3 3 4 , then the value of C is

1) –2 2) 3 3) 2 4) 4

Sol: 2; C

33 3 4 3 ( ) 4

8 3c 2 4 6c 12 c 2

47. If the slope of the tangent to the circles 2 2S x y 13 0 at (2, 3) is m, then the point

1m,

m

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

Sol: 2 2x y 13

Tangent at (2, 3) is x 2 y 3 13 0

M = slope = 2

3

1 2 3

m, ,m 3 2

2 3 4 9 16 81

S , 13 13 03 2 9 4 36


Page No : 21

48. 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

Sol: T,R,I,C,K

C arranged in 4! Ways using T,R,I,K = 24

49. The angle between the curves 2x 8y and xy 8 is

1) 1 1tan

3

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

3

Sol: 2 8x 8y; xy 8 y

x

3x 64 x 4, y 2 x,y 4,2

1 24,2 4,2

1m 1, m

2

1tan 3 tan 3

50. f : ( ,0] [0, ) is defined as 2f x x . The domain and range of its inverse is

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

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

3) Domain of 1f [0, ), Range of 1f [0, )

4) 1f does not exist

Sol: 2 2f x x y x x y x y

1f x x

Domain of 1f [0, )


Page No : 22

Range of 1f ( ,0]

51. If a,bandc are unit vectors such that a b c 0 and a,b ,3

then

a b b c c a

1) 3

2 2) 0 3)

3 3

2 4) 3

Sol: a b c 0 a b b c c a

3 3

a b 3 a b2

52. The differential equation of the simple harmonic motion given by x Acos(nt ) is

1) 2

2

2

d xn x 0

dt 2)

22

2

d xn x 0

dt 3)

2

2

dx d x0

dt dt 4)

2

2

d x dxnx 0

dt dt

Sol: x Acos nt

dx

Asin nt ndt

2

2 2

2

d xAcos nt n n x

dt

22

2

d xn x 0

dt

53. If a and b are unit vectors and is the angle between them, then a b is a unit vector

when cos

1) 1

2

2)

1

2 3)

3

2 4)

3

2

Sol: a,b a b 1


Page No : 23

2

a b 1

1 1 2a.b 1

1

cos2

54. A parallelogram has vertices A 4,4, 1 ,B 5,6, 1 ,C 6,5,1 and D x, y,z . Then the

vertex D is

1) (5, 1, 0) 2) (5, 0, 1) 3) (5, 3, 1) 4) (5, 1, 3)

Sol: fourth vertex D = A + C – B = (5, 3, 1)

55. If 2 22x 10xy 2 y 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) 7

10,2

4) 3

10,2

Sol: 2 2

hf bg gh af 7, 10,

ab h ab h 2

56. If ranks of 2

x x x

x x x

x x x 1

is 1, then

1) x 0 or x 1 2) x 1 3) x 0 4) x 0

Sol: By verification x = 0

57. If the vectors ˆ ˆ ˆ ˆ ˆ ˆa i j k, b i j 2k and ˆ ˆ ˆc xi x 2 j k are coplanar, then x

1) 1 2) 2 3) 0 4) –2

Sol:

1 1 1

1 1 2 0 x 0

x x 2 1


Page No : 24

58. In order to eliminate the first degree terms from the equation

2 24x 8xy 10y 8x 44y 14 0 the point to which the origin has to be shifted is

1) (–2, 3) 2) (2, –3) 3) (1, –3) 4) (–1, 3)

Sol: f

8x 8y 8 0 x y 1 0x

(-2,3) satisfies the above equation

59. 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) 5a

a,3

4) (a, a)

Sol: Equation of perpendicular A (2, 3) B(5, 6) is

2x 3 2y 3 4 9 25 36

x y 8

2 2 2 2

1 2 1 2c c r r 18 2a a 3

60. If

1 2

1 2

1 2

costan k cot , then

cos

1) 1 k

1 k

2)

1 k

1 k

3)

k 1

k 1

4)

k 1

k 1

Sol: 1

2

tanK

cot

1 1

1 1

tan cot K 1

tan cot K 1


Page No : 25

61. Let CH3 CH CH2 OH

CH3 and b i 3 j 2k . Then the volume of the parallelopiped having

coterminous 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

Sol: a b c a b c cos

11i 7 j 5k 2

121 49 25 2 2 195

62. The local maximum of 3 2y x 3x 5 is attained at

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

Sol: 2f ' x 3x 6x 0 x 0,x 2

f '' x 6x 6 f '' 0 0,f '' 2 0

F is maximum at x = 0

63. In the expansion of n

1 x , the coefficients of thp and th

p 1 terms are respectively p and

q, then p + q =

1) n+3 2) n+2 3) n 4) n+1

Sol: p 1 pc cn p, n q

p

p 1

c

c

nq n p 1p q n 1

p n p

64. If 2 2

sin x if x 0

x a if 0 x 1f x

bx 2 if 1 x 2

0 if x 2

is continuous on [R, then a + b + ab =


Page No : 26

1) –2 2) 0 3) 2 4) –1

Sol: At x = 0

LL = 0, RL = a2 2a 0 a 0

At x=1, 2LL 1 a ,RL b 2

21 a b 2 1 b 2 b 1

At X = 2

LL = 2b + 2, RL = 0 2b 2 0

Now a + b + ab = –1

65. If 1

ecosh x 2log 2 1 , then x

1) 1 23) 2 3) 4 4) 3

Sol: 2

1

e ecosh x log 2 1 log 3 2 2

log 3 9 1 x 3

66. For any integer n

K 1

n 1, K K 2

1) n n 1 n 2

6

2)

n n 1 2n 7

6

3)

n n 1 2n 1

6

4)

n n 1 2n 8

6

Sol: n n

2

K 1 K 1

K 2 K

n n 1 2n 1 n n 1 n n 1 n n 1 2n 7

2 2n 1 66 2 6 6

67. The foci of the ellipse 2 225x 4y 100x 4y 100 0 are


Page No : 27

1) 5 21

, 210

2)

5 212,

10

3) 2 21

, 210

4)

2 212,

10

Sol: 2 225x 4y 100x 4y 100

2 225 x 4x 4 y y 100

2

2 125 x 2 4 y 1

2

2

2

2 2

1y

x 2 21

1 1

5 2

b > a

1 1

4 25e1

4

5 4 21

4100 25

=

21

5

1 21

s,s ' , be 2,2 10

68.

72

1 cos isin12 12

1 cos isin12 12

1) 0 2) –2 3) 1 4) 1

2

Sol:

2

2

1 cos isin 2cos i2sin cos12 12 24 24 24

2cos i2sin cos1 cos isin24 24 2412 12


Page No : 28

=

ciscos isin244 4

cos isin cis4 4 24

cis cis24 24 12

Now, 72

cis cis6 1 i 0 112

69. If the range of the function f x 3x 3 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

Sol: f (x) 3x 3

Range of f {3, 6, 9, 18}

Verification

f 1 3 1 3 3 3 0

But 0 Range of f

1 Domain

70. In ABC, if oa 1, b 2, C 60 then

2 24 c

1) 6 2) 3 3) 3

2 4) 9

Sol:- 1

absin c2

3

2

2 2 2c a b 2abcosc

1 4 2

3 2 24 c 3 3 6


Page No : 29

71. If the magnitude 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

Sol: a 3, b 4, a b 5

era b

2 22

a b a b 2a.b 9 16 0 25

a b 5

72. If 21

f x cos xdx f x C2

and f 0 f 0 0, then f ' 0

1) 1 2) –1 3) 0 4) 2

Sol: 21

f x .cos xdx f x c2

Diff. w.r.to x on both sides

1

f x cos x .2f x .f ' x2

cos x f ' x

Put x = 0,

f ' 0 cos0 1

73. If and are the roots of the equation 2ax bx c 0 and the equation having roots

1

and

1

is

2px qx r 0, then r

1) a 2b 2) ab bc ca 3) a b c 4) abc


Page No : 30

Sol: 2f x 0 ax bx c 0

, are roots of f x 0

1 1

,

are roots of

2px qx r 0

Let 1

x

1 x

x 1

1 x 1

1

1 x

21 1 b

f 0 a c 01 x 1 x 1 x

2

a b 1 x c 1 x 0

r a b c

74. If A ,B3 6

are the points on the circle represented in parametric form 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 2 4) 6 3 1

Sol: Centre C = (0, 0) r = 12

1 1A x rcos , y rsin3


Page No : 31

1 3

0 12 ,0 122 2

6,6 3

3 1

B 12 ,126 2 2

6 3,6

Length of chord 2 2

AB 6 3 6 6 3 6

2

2. 6 3 6

6 3 6 2

6 3 1 2

6 6 2

75. 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 2 2ax 13xy 7y x 23y 6 0 is

1) 1 5

cos218

2) 1 1

cos10

3) 1 5

cos173

4) 1 1

cos5

Sol: xy x y 1 0 (1)

x ay 3 0 (2)

x y 1 y 1 0

x 1 y 1 0

x 1,y 1


Page No : 32

point of intersection = (1, 1)

(1), (2) are concurrent passing through (1, 1)

1 a 3 0 a 2

Now, 2 22x 13xy 7y x 23y 6 0

1

2 2

a b 5 1 1cos cos

250 10 10a b 4h

76. The number of solutions of cos2 sin in 0,2 is

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

Sol: 2cos2 sin 1 2sin sin

2sin 1 sin 1 0

1

sin ,sin 12

Number of solutions is 3

77. 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) 65

8 3) 4 4) 69

Sol: a = 13, b = 14, c = 15, s = 21

84

r 4

8R + r = 65

2 4 692

78. If A and B are the variances of the 1st ‘n’ even numbers and 1

st ‘n’ odd numbers

respectively then


Page No : 33

1) A = B 2) A > B 3) A < B 4) A = B + 1

Sol: Variance is independent of origin

A B

79. If the line x y 4K is a tangent to the parabola 2y 8x at P, then the perpendicular

distances of normal at P from (K, 2K) is

1) 5

2 2 2)

7

2 2 3)

9

2 2 4)

1

2 2

Sol: x y 4k y x 4k

m = 1, c = 4k

It is a tangent to the parabola 2 8

y 8x a 24

a 2 1

c 4k km 1 2

1

x y 4 x y 2 02

Point of contact 2

a 2ap , 2,4

m m

Equation of normal at p 2,4 is 3y mx 2am am

Slope of tangent at p is m = 1

Slope of normal at p is -1

Equation of normal at p is y x 6 x y 6 0

Perpendicular distance from (k, 2k) = 1

,12

to x y 6 0


Page No : 34

Is

12 6

92

2 2 2

80. If A and B are events having probabilities, P(A) = 0.6, P(B) = 0.4 and A B 0, then the

probability that neither A nor B occurs is

1) 1

4 2) 1 3)

1

2 4) 0

Sol: p A 0.6, p B 0.4; p A B 0

p A B 1 p A B

1 – 1 = 0

PHYSICS

81. A force F is applied on a square plate of length L. If the percentage error in the

determination of L is 3% and in F is 4%, the permissible error in the calculation of

pressure is

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

Sol:- F

PA

2

F

L

100 100 2 100P F L

P F L

4% 2 3%

10%


Page No : 35

82. 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 filed at a point in the cavity, a distance ‘r’ from center is

1) zero 2) 2

04

Q

R 3)

2

04

q

r 4)

2

04

q Q

r

Sol:

r

q

p

0

inqEds

2

0

1

4

q

r

83. A swimmer wants to cross a 200m wide river which is flowing at a speed 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) 200m 2) 400m 3) 600m 4) 800m

Sol:- man stream

W drift

V V

200

1 2

drift

400drift m

84. A coil having ‘n’ turns and resistance R is connected with a galvanometer of resistance

4R . This combination is moved in time ‘t’ seconds from a magnetic flux

1 2Weber to Weber. The induced current in the circuit is


Page No : 36

1) 2 1

5Rnt

2)

2 1

5

n

Rt

3)

2 1

Rnt

4)

2 1n

Rt

Sol:- e

iR

R t

2 1

5Rt

85. A simple pendulum of length 1m is freely suspended from the ceiling of an elevator. The

time period of small oscillations as the elevator moves up with an acceleration of 22 /m s is

(use 210 /g m s )

1) 5

s

2) 2

5s 3)

2s

4)

3s

Sol:- 2l

Tg a

1

212

1

22 3

3

86. 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 , the maximum potential difference between points on the ball is

1) sinr B v 2) sinB v 3) 2 sinr B v 4) 2 cosr B v


Page No : 37

Sol:- sine Blv

2 sinB r v

87. Each of the six ideal batteries of emf 20V is connected to an external resistance of 4 as

shown in the figure. The current through the resistance is

4R

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

Sol:- No answer

88. The energy that should be added to an electron to reduce its de-Broglie wavelength from 1

nm to 0.5 nm 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

Sol:- 1

KE

2

1KE

2 2

2 1

1 2

1

0.5

KE

KE

2 14KE KE

13KE KE


Page No : 38

89. In the given circuit, a charge of 80 C is given to upper plate of a 4 F capacitor. At

steady state the charge on the upper plate of the 3 F capacitor is

3 F2 F

4 F

80 C

1) 60 C 2) 48 C 3) 80 C 4) 0 C

Sol:- 1 2: 2 :3Q Q

2

380

5Q

48 C

90. 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 1m 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

Sol:- stress

strainY

stress

e lY

8

11

101

2 10


Page No : 39

45 10 m

0.5mm

91. 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 1kg, the angle of inclination is 030 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 030 is less than angle of repose 2) 1N

3) 3.3N 4) 16.3N

Sol:-

Fcosmg

sinmg

N

f

sin cosmg F mg

sin

cosmg

F mg

sin

cosmg

1 3

102 0.2 2

5 3

102 2


Page No : 40

5 5 3

5 5 1.732

16.34

92. A metre scale made of steel reads accurately at 025 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

6 011 10 / C )

1) 0 019 31C to C 2)

0 025 32C to C 3) 0 018 25C to C 4)

0 018 32C to C

Sol:- l l t

l

tl

5

6

6 10

1 11 10

05.45 C

0 019 31C to C

93. 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

Sol:-

inducedi Supports 1i

94. 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


Page No : 41

lower surface of the glass plate, the ratio of maximum to minimum intensity in the

interference region of the reflected light is

1)

2

1 3

2 8

1 3

2 8

2)

2

1 3

4 8

1 3

2 8

3) 5

8 4)

8

5

Sol:-

0

3

4I 0

3

8I

0

3

8I

0

4

I

0I

01

4

II

2 0

3

8I I

2

1 2max

2

min1 2

I II

I I I

2

1 3

2 8

1 3

2 8

95. A thermocol box has a total wall area (including the lid) of 21.0m and wall thickness of 3

cm. It is filled with ice at 00 C . If the average temperature outside the box is

030 C

throughout the day, the amount of ice that melts in one day is

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

Sol:- 21A m

53 10L


Page No : 42

23 3 10l cm m 24 60 60t

030 0 30 C

Q KA

t l

5

2

3 10 0.03 130

24 60 60 3 10

m

8.64m kg

96. Which of the following is emitted when 239

94 Pu decays into 235

92 U ?

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

Sol:- 239 4 235

94 2 92Pa He U

particle

97. An AC generator producing 10V(rms) at 200 rad/s is connected in series with a

50resistor, a 400 mH inductor and a 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

Sol:- , 200, 50 , 400 , 20010 W R L mH c FE V

2 22 250 80 25L CZ R X X

74.3Z

10

0.1345974.3

EI A

Z

0.1345 80 10.76L LE IX V


Page No : 43

98. A wire has resistance of 03.1 30at C and

04.5 100at C . The temperature coefficient of

resistance of the wire is

1) 0 10.0012 C

2) 0 10.0024 C

3) 0 10.0032 C

4) 0 10.0064 C

Sol:- 2 1

1 2 2 1

R R

R t R t

4.5 3.1

3.1 100 4.5 30

1.4

310 135

0.008

3 0 18 10 C

99. 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

Sol :- velocity half second before maximum height

= velocity half second after maximum height (Return Journey )

= 0+9.8 ×1/2= 4.9 m/s

100. 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

Sol :- energy given to hydrogen atom

= difference in energy levels from

n = 1 to n = 3 states


Page No : 44

= 13.6 2 2

1 1

1 3

= 12 .1 eV

101. Consider the motion of a particle described by x = a cos t, y = a sin 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

Sol :- path is circular in x – y plane

2 2

2 2

2 2cos sin 1

x y

a a

In one revolution , the particle moves

A distance of 1 unit along z-axis

1dz

dt

Path is helix

102. Consider a reversible engine of efficiency 1

6. When the temperature of the sink is reduced

by 62ºC, 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) 99ºC and 10ºC 4) 200 ºC and 37ºC

Sol :- 1 21

1

1(1)

6

T T

T

1 2

2

1

62 2 1(2)

6 3

T T

T

From (1) and (2)

1 2372 310K and T KT


Page No : 45

103. 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 1 m. The position ( ')s , nature and

magnification (m) of the image are

1) 's = 0.375 m, Virtual, upright , m = 0.25 2) 's = 0.375 m, Real, inverted , m = 0.25

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

Sol :- 1 1 1 2

v u f R

1 1 1

2 0.3753 / 2 1

v mv

= 3/8 m, image is virtual

3 / 8 1

0.253 / 2 4

v

um

104. 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 ºC to 24ºC at a constant pressure of 1.0 atm is

[ 1.4 tan 8.314 / ]airUse and Universal gas cons t J mol K

1) 51.9 10 J 2) 51.9 10 J 3) 54.2 10 J 4) 50.7 10 J

Sol :- dv = vnc dT

32 10 [10]0.4

R

52 8.31410

4

54.2 10

105. A ball is thrown at a speed of 20 m/s at an angle of 30º with the horizontal. The maximum

height reached by the ball is (use g = 10m/s2)

1) 2 m 2) 3 m 3) 4 m 4) 5 m


Page No : 46

Sol :- H =

21

20 202

520

m

106. A horizontal pipeline carrying gasoline has a cross-sectional diameter of 5 mm. If the

viscosity and density of the gasoline are 6×10-3

Poise and 720 kg/m3 respectively, the

velocity after which the flow becomes turbulent is

1) > 1.66 m/s 2) > 3.33 m/s 3) > 1.6×10-3

m/s 4) > 0.33 m/s

Sol :- d

R

R

d

3 4

5

3

2 10 6 15 110

720 5 10 6

3 4

3

2 10 6 10 1 1100 0.333

720 5 10 300 3

107. A piece of copper and a piece of germanium are cooled from room temperature to

80K.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

Sol :- ( )cuR decrease

( )geR increase


Page No : 47

108. 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) 21

1

nSi

Sin

2) 1

1

2

nSi

Sin

3) 1

1

2

4) 1

Sol :- 1 0

1 2 1

1 2

n

2

Si

Sin

22 1

1

nSi

Sin

109. An amplitude modulated signal consists of a message signal of frequency 1 KHz and peak

voltage of 5V, modulating a carrier frequency of 1 MHz and peak voltage of 15V. The

correct description of this signal is

1) 6 35[1 3sin(2 10 )]sin(2 10 )t t 2) 3 6115[1 sin(2 10 )]sin (2 10 )

3t t

3) 3 6[5 15sin(2 10 )]sin(2 10 )t t 4) 6 3[15 5sin(2 10 )]sin(2 10 )t t

Sol :- message wave signal = 5 sin (20×103t)

Carrier wave signal = 15 sin (20×106 t)

Modulated wave signal

3 6(15 5sin(2 10 )sin(2 10 )t t

3 6115 1 sin(2 10 ) sin(2 10 )

3t t

110. Which of the following principles is being used in Sonar Technology ?

1) Newton’s laws of motion 2) Reflection of electromagnetic waves


Page No : 48

3) Laws of thermodynamics 4) Reflection of ultrasonic waves

Sol :- sonar technology uses Doppler effect of ultrasonic waves

111. A particle of mass M is moving in a horizontal circle of radius R with uniform speed v .

When the particle moves from one point to a diametrically opposite point, its

1) momentum does not change 2) momentum changes by 2M v

3) kinetic energy changes by 2

4

Mv 4) kinetic energy changes by 2Mv

Sol :- change in momentum

= mv – (-m v)

= 2 mv

112. A billiard ball of mass ‘M’ moving with velocity ‘ v 1’ 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) 0º 2) 30º 3) 90º 4) 45º

Sol :- 0º If collision is head on

90º If collision is oblique

113. 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 r1 and r2

respectively. The angular momentum of the planet relative to the centre of the star is

1) 1 2

1 2

2GMrrm

r r 2) 0 3)

CH3 CH CH2 OH

CH3

4)

1

1 2 2

2GMmr

r r r

Sol :- From law of conservation of angular momentum


Page No : 49

1 1 2 2mv r mv r

1 12

2

(1)v r

vr

From law of conservation of total mechanical energy

- 2 2

1 2

1 2

1 1(2)

2 2

GMm GMmmv mv

r r

From equations – (1) and (2)

21

1 2 1

2

( )

Gmr

r r rv

Angular momentum

1 1rL mv

1 2

1 2

2GMrr

r rm

114. Consider a frictionless ramp on which a smooth object is made to slide down from an

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

Sol :- from conservation of energy

mgh = mgd


Page No : 50

hd

115. A generator with a circular coil of 100 turns of area 2×10-2

m2 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

Sol :- maximum emf

0 NBAe

2 22

2 507

100 0.01 2 10

= 6.28 V

116. A sound wave of frequency ‘ v ’ 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 of

the reservoir is 340 / ; 148 /air waterV m s V m s

1) > v Hz 2) < v Hz 3) v Hz 4) 0

Sol :- frequency of sound remains constant

117. 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 – type semiconductor

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

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

Sol :- Majority charge carries in n-type semi conductor are electrons

118. The deceleration of a car traveling on a straight highway is a function of its instantaneous

velocity ‘ v ’ given by w a v , where ‘a’ is a constant. If the initial velocity of the car is


Page No : 51

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) 3 1

,2 2

m sa a

3) 3

,2 2

a am s 4)

2 2,

3m s

a a

Sol :- No Option

119. A current carrying wire in its neighbourhood produces

1) electric field 2) electric and magnetic fields

3) magnetic filed 4) no field

Sol :- Current carrying conductor produces magnetic field in its neighbourhood

120. Consider a particle on which constant forces ˆˆ2 3F i j k N and 2ˆˆ4 5 2F i j k N act

together resulting in a displacement from position 1ˆ20 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

Sol :- 1 2F F F

ˆˆ ˆ5 3i j k

2 1s r r

ˆˆ ˆ20 15 7s i j k cm

.W F S

2100 45 7 10

0.48J

CHEMISTRY

121. Which of the following conditions are correct for real solutions showing negative deviation from

Raoult's law?


Page No : 52

1) 0; 0Mix Mix

H V 2) 0; 0Mix Mix

H V

3) 0; 0Mix Mix

H V 4) 0; 0Mix Mix

H V

Sol:- 4) 0; 0Mix Mix

H V

122. Nitration of phenyl benzoate yields the product

1) 2)

3) 4)

Sol:- 2)

O

6 5O C C H is ortho and para director

123. The electronic configuration of 59Pr (praseodymium) is

1) 2 1 2

54[ ]4 5 6Xe f d s 2)

1 2 2

54[ ]4 5 6Xe f d s 3)

3 2

54[ ]4 6Xe f s 4)

3 2

54[ ]4 5Xe f d

Sil:- 3) Conceptual

124. Which of the following is the most basic oxide ?

1) SO3 2) SeO3 3) PoO 4) TeO


Page No : 53

Sol:- 3) PoO is more basic

125. The element that forms stable compounds in low oxidation state is

1) Mg 2) Al 3) Ga 4) Tl

Sol:- 4) ‘Tl’ due to inert pair effect.

126. 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

Sol:- 2) 143, 117, 74, 64 in a period from left to right atomic radius decreases

127. Reaction of calgon with hard water containing Ca2+

ions produce

1) 2

2 6 18[ ]Na CaPO

2) 2 4 3( )Ca PO 3)

3CaCO 4)

4CaSO

Sol:- 1) 2

4 6 18[ ]Na CaPO

+ 2Ca 2

2 6 18[ ]Na CaPO

128. Which of the following statement is true

1) The pressure of a fixed amount of an ideal gas is proportional to its temperature only

2) Frequency of collisions increases in proportion to the square root of temperature

3) The value of van der Waal’s constant ‘a’ is smaller for ammonia than for nitrogen

4) If a as is expanded at constant temperature, the kinetic energy of the molecules decrease

Sol:- 2) Frequency of collisions increases in proportion to the square root of temperature

129. 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 aluminium hydride


Page No : 54

Sol:- 3) reduction with lithium aluminium hydride

2

3 2 2 5 3 29 9

DIBAL H

H OCH CH C O C H CH CH CHO

O

130. Consider the following electrode process of a cell,

2

1

2Cl Cl e

MCl e M Cl

If EMF of this cell is –1.140 V and E0 value of the cell is –0.55V at 298K, the value of the

equilibrium constant of the sparingly soluble salt MCl is in the order of

1) 10–10

2) 10–8

3) 10–7

4) 10–11

Sol:- 1) 0 0.059

logE E Kspn

0.059

1.14 0.55 log1

Ksp 1010Ksp

131. 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

Sol:- 1) Adsorption is exothermic Process and S < 0

132. Consider the single electrode process 2

4 4 2H e H 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) 1 M 2) 10M 3) 0.1 M 4) 0.01 M

Sol:- 3) 0.1 M


Page No : 55

0 2

4

0.059log

pHE E

n H

4

0.059 10.059 0 log

4 H

110 0.1H M

133. Which of the following elements has the lowest melting point ?

1) Sn 2) Pb 3) Si 4) Ge

Sol:- 1) Sn C Si Ge Pb Sn

134. The number of complementary Hydrogen bond(s) between a guanine and cytosine pair is

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

Sol:- 4) Guanine pairs up with cytosine by three hydrogen bonds.

135. Given 0

fH for

2( ) ( ),

g gCO CO and

2( )H O g are –393.5, –110.5 and –241.8 kJ mol

–1,

respectively. The 0

fH [in kJ mol

–1] for the reaction

2 2( ) ( ) 2( ) ( )

g gCO g H CO H O g is

1) 524.1 2) –262.5 3) –41.7 4) 41.2

Sol:- 4) tanproducts reac ts

H H H = 41.2

136. Which among the following is the strongest acid?

1) HF 2) HCl 3) HBr 4) HI

Sol:- 4) Down the hydrides bondlength incrases bond energy decrases acidic nature incrases

137. The species having pyramidal shape according to VSEPR theory is

1) SO3 2) BrF3 3) SiO32-

4) OsF2

Sol:- 4) OSF2 Central atom sulphur contain 3 b.p and 1 l.p hence OSF2 is pyramidal. But it is given

as OsF2 it is wrong question.

138. The bonding in diborane (B2H6) can be described by


Page No : 56

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

Sol:- 1)

B B

H

H

H

H H

H

139. The monomers of Buna-S rubber are

1) Isoprene and butadiene 2) Butadiene and phenol

3) Styrene and butadiene 4) Vinyl chloride and sulphur

Sol:- 3) Conceptual

140. Heating a mixture of Cu2O and Cu2S will give

1) CuO + CuS 2) Cu + SO3 3) Cu + SO2 4) Cu(OH)2 + CuSO4

Sol:- 3) 2 2 22 6Cu O Cu S Cu SO

141. 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

Sol:- 3) 2

13.6/E eV atom

n

n = 2 (first excited state) =

2

13.63.4

2eV

142. Which of the following are the correct representations of a zero order reaction, where A

represents the reactant?


Page No : 57

1) a, b, c 2) a, b, d 3) b, c, d 4) a, c, d

Sol:- 2) Conceptual

143. The set representing the right order of ionic radius is

1) Li+ > Na

+ > Mg

2+ > Be

2+ 2) Mg

2+ > Be

2+ > Li

+ > Na

+

3) Na+ > Mg

2+ > Li

+ > Be

2+ 4) Na

+ > Li

+ > Mg

2+ > Be

2+

Sol:- 4) As charge on cation increases size decreases and down the group size increases

144. 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 complex form

Sol:- 1) Conceptual

145. The reactivity of alkyl bromides

A) CH3 CH2 Br B)

CH3

CH3

CH Br

C)

CH3

CH3

C Br

CH3

D) CH3Br

Towards iodine ion in dry acetone decrease in the order

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


Page No : 58

Sol:-

3 3 2 3 3 3CH Br CH CH Br CH CH CH CH C Br

Br 3CH

3CH

146. Optically active CH2CH3 CH CH3

OH

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) CH2CH3 CH CH2 2)

CHCH3 CH CH2

3) CHCH3

CH2 OH

CH3

4) CH3 CH2 OHCH2 CH2

Sol:- 2) CHCH3 CH CH2 Dehydration takes place to form stable alkene through the formation

of stable corbocation.

147. Commercially available 2 4H SO H is 98 gms 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 is 98

g mol-1

)

1) 500 m 2) 20 molal 3) 50 m 4) 200 m

Sol:- molality 2 4

2 4

. 1000

. . .

wt of H SO

mol wt of H SO wt of water

98 1000500

98 2

148. Cylohexylamine and aniline can be distinguished by

1) Hinsberg test 2) Carbylamine test 3) Lassaigne test 4) Azo dye test

Sol:- 4) Azo dye test is given aromatic amine only.

149. ________ is a potent vasodilator.

1) Histamine 2) Serotonin 3) Codeine 4) Cimetidine

Sol:- 1) Conceptual


Page No : 59

150. Standard Enthalpy (Heat) of formation of liquid water at 250C is around

H2(g)+1

2O2(g) H2O(l)

1) -237 kJ/mol 2) 237 kJ/mol 3) -286 kJ/mol 4) 286 kJ/mol

Sol:- 3) 0 286 /fH water kJ mole

151. The alcohol that reacts faster with Lucas reagent is

1) CH3 CH2 CH2 CH2 OH

2)

CH3 CH2 CH CH3

OH

3)

CH3 CH CH2 OH

CH3 4)

CH3 C OH

CH3

CH3

Sol:- 4) 30 alcohol reacts with lucas reagent immediately.

152. 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 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

Sol:- 2) 3 12 22 11 2 2 2 2 348 5 24 36 55 24KNO C H O N CO H O K CO

153. Which of the following element is purified by vapour phase refining?

1) Fe 2) Zr 3) Cu 4) Au

Sol:- 2) Van Arkel method for refining Zr, Ti and Monds process for Ni on vapour phase refining

methods.

154. 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


Page No : 60

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

Sol:- 3) hydrogen and Helium exhibit heating effect during Joule-Thomson expansion due to low

inversion temperature.

155. The vapour pressure of a non-ideal two component solution is given below

1) 2)

3) 4)


Page No : 61

Sol:- 1) Boiling point 1

vapour pressure

156. Cyclopentadienyl anion is

1) benzenoid and aromatic 2) non-benzenoid and aromatic

3) non-benzenoid and non-aromatic 4) non-benzenoid and anti-aromatic

Sol:- 2) Non Benzenoid Aromatic

157. Oxidation of cyclohexene in presence of acidic potassium permanganate leads to

1) glutaric acid 2) adipic acid 3) pimelic acid 4) succinic acid

Sol:- 2)

Kmno4

H+ COOH

COOH

158. How many emission spectral lines are possible when hydrogen atom is excited to nth

energy

level?

1) ( 1)

2

n n 2)

( 1)

2

n 3)

( 1)

2

n n 4)

2

4

n

Sol:- 3) Number of spectral lines = 1

2

n n

159. The bond length (pm) of F2, H2, Cl2 and I2, respectively is

1) 144,74,199,267 2) 74,144,199,267 3) 74,267,199,144 4) 144,74,267,199

Sol:- 1) Bond length atomic size

160. 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


Page No : 62

Sol:- 2) Number of particles in ccp = 4. Hence number of tetrahedral and octahedral voids are 8 and 4

respectively

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