question paper with solutions - sri gayatri

S R I G AYAT R I E D U C A T I O N A L I N S T I T U T I O N S - T E L A N G A N A

12 May 2017 TS EAMCET 2017 - ENGINEERING PAPER (CODE-) 1

Question Paperwith Solutions

CODE-A


12 May 2017 TS EAMCET 2017 - ENGINEERING PAPER (CODE-A) 1

MATHS

1. If tan 020 , then 0 0

0 0

tan160 tan1101 (tan160 )(tan110 )

1) 21

2

2)

21

3) 21

4) 21

2

Key: 4

Sol: .2

1tan 20 cot 20 1

1 1 2 2

2 . Consider the circle 2 2 6 4 12x y x y .The equation of a tangent to this circle that is parallel

to the line 4 3 5 0x y is1) 4 3 10 0x y 2) 4 3 9 0x y 3) 4 3 9 0x y 4) 4 3 31 0x y Key: 4

Sol: . 2( ) 1y f m x g r m

4 162 ( 3) 5 13 9

y x

4 252 33 3

y x

3 6 4 12 25y x

4 3 6 25x y

4 3 19 0x y

3. The mean deviation from the mean 10 of the date 6,7,10,12,13, ,12,16 is1) 3.5 2) 3.25 3) 3 4) 3.75Key: 2

Sol: .6 7 10 12 13 17 16 10

8x

4 ; M.D= 3.25ix x

n

4. Match the followingList -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

( )a

f x dx c) 0

( ) ( )a

f x f x dx IV. ( )

a

af x dx

d) 0

e) 0

( )a

f 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 cKey: 1Sol: .Conceptual

5. If f is differentiable , ( ) ( ) ( )f x y f x f y for all ', , (3) 3, (0) 11,x y R f f then '(3)f

1) 3

11 2) 113 3) 8 4) 33

Key: 4

Sol: . '(0) (3) 3(11) 33f f

6. 2 20 4cos 9sinxdxx x

1) 2

12

2) 2

4

3) 2

6

4) 2

3

Key: 1

Sol: .G.I = 2

2ab

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 is1) 1.6 2) 0.24 3) 0.84 4) 0.75Key: 3

Sol: Let. 0 0.4 0.6 0.6 0 1.6 2 20 0.4 1.2 1.8 0 (1.6) 0.84

8. 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 0.50.5 0 00.5 0 0

4)

0 0.5 00.5 0 0.50 0.5 0

Key: 2

Sol: .2

TA AC

9. If a

is a unit vector, then 22 2 ˆˆ ˆa i a j a k

1) 2 2) 4 3) 1 4) 0Key: 1



Sol: .22 2 2ˆˆ ˆ 2 2a i a j a k a

10. 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: 4

Sol: .Required probability = 3 3 3

3

5 3 41

12C C C

C

= 4144

11. The radical centre of the circles2 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: 4Sol: .Equations of radical axies of ( 1) and (2) and (2) and (3) are

3 0, 4 2 1 0x y x y by solving these two equations weget R.C= 7 11,6 6

by verification R.C lies on 18x-12y+1=012. If cos cot 2017,ec then quadrant in which lies is

1) I 2) IV 3) III 4) IIKey: 4Sol: . cos cot 2017ec .................. (1 )

1cos cot2017

ec .................... ( 2)

then cos 0&cot 0ec

2Q

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

1) 21 ( ) ( )2

xe f x g x C 2) 21 ( ) ( )2

xe f x g x C

3) 21 (2 ) ( )2

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

xe f x g x C

Key: 2

Sol: .G.I = 2 2 '( ) ( )x xe f x dx e f x dx 2 ( ) ( )xe f x dx g x

22 '( ) ( ) ( )

2

xx ef x e dx f x dx g x



22 '1( ) ( ) ( )

2 2

xxef x e f x dx g x

2 1( ) ( )2 2

xef x g x

21 ( ) ( )2

xf x e g x C

14. If (5,3), (3, 2)A B and a point P is such that the area of the triangle PAB is 9, then the locusof P represents1) a circle 2) a pair of coincident lines3) a pair of parallel lines 4) a pair of perpendicular linesKey: 3Sol: .Area of 9lePAB

5 2 37 5 2 1 0x y x y

then locus represents a pair of parallel lines15. 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 torigin. Then the lines is represennted by the equations

1) 2 3 5x y 2) 2x y 3) 2x y 4) 2 5x y Key: 4

Sol: .Let the equation be 12

x ya a

given lr distance = 1

2

15a

2 5a

required line is 2 5x y

16. Let S and 'S be the foci of an ellipse and B be one end of its minor axis. If 'SBS is an isoscelesright angled triangle then the eccentricity of the ellipse is

1) 12 2)

12 3)

32

4) 13

Key: 1

Sol: . 45 bTanae

12

e



17. For the parabola 2 6 2 5y y x I ) the vertex is (-2,-3) II) the directrix is y+3=0Which of the following is correct?1) Both I and II are correct 2) I is true , II is false3) Both I and II are false 4) I is false, II is trueKey: 2

Sol: .Given parabola rediuced in the form of 23 2( 2)y x

vertex = -2,-3equation of directrix is 0x h a

18. If 2

22

5 ,2 11 ( 2)

x A Bx Cx xx x

then A+B+C=

1) -1 2) 25 3)

35

4) 0

Key: 3Sol: . 2 25 ( 1) ( )( 2)x A x Bx C x by comparing like term on both sides then weget

9 4 8, ,5 5 5

A B C

19. ( )(1 2 )x iy i is (1 ),i then

1) 1x iy i 2) 1

1 2ix iyi

3)

11 2

ix iyi

4)

11

ix iyi

Key: 2

Sol: .Given 1 2 1x iy i i

by comparing real and imaginary parts we get2 1& 2 1x y x y

by solving these equations weget 3 1,5 5

x y

by verification 1

1 2ix iyi

1 1 21 2 1 2

i ix iyi i

35

i

20. 4 2 xx 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



Sol: .G.I = 2 2 2 2 2

4 3 24 12 24 242 4 8 16 32

x x x x xe e e e ex x x x C

24 3 2(2 4 6 6 3)

4

xe x x x x C

21. The sides of a triangle are in the ratio 1: 3 : 2 . Then the angles are in the ratio1) 1:2:3 2) 1:2:4 3) 1:4:5 4) 1:3:5Key: 1

Sol: .Given : : 1: 3 : 2a b c

1 23a b c k

by using the formulas cos , ,A CosB CosC we get : :A B C=1:2:3

22. The sum of the complex roots of the equation 3( 1) 64 0x is1) 6 2) 3 4) 6i 4) 3iKey: 2

Sol: . 1/ 3 21 4( 1) 4( 1, , )x 24, 4 , 4

21 4, 4 , 4x 23,1 4 ,1 4x

sum of complex roots is = 21 4 1 4 6

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

1) 94 2) 9 3)

92 4)

97

Key: 3Sol: .By solving given equations weget 1, 2y y

required area = 2 2

1

922

y y dy

24. 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

Sol: . a i xk zk

a j xk zk

a k x j yi

then we get x+y+z



25. If the imaginary part of 2 1

1z

iz

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

plane is1) a circle 2) a parabola 3) a straight line 4) an ellipseKey: 3

Sol:

2 12 11 1 1

x iyzz i x iy

by simplyfing we get the equation 2 2 0x y it repregents a straight line.

26. Let : ( 1,1)f R be a differentiable function with (0) 1f and ' (0) 1f . If2( ) ( (2 ( ) 2))g x f f x , then '(0)g

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

Sol: 22 2g x f f x

1 2 2 2g x f f x 1 12 2 2f f x f x

Now 1 1 10 2 2 0 2 2 0 2 2 0g f f f f f

4 27. 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 are1) -35,42 2) 35,28 3) 42,-28 4) 28,-42Key: 4

Sol: 3 4

79 16

c

7 35c

28, 42c c

28. The solution of dy x ydx x y

is

1) 1 2 2tan logx x y C

y

2) 1 2 2tan logy x y C

x

3) 1 2 2sin logy x y C

x

4) 1 2 2cos logy x y C

x

Key: 1

Sol: .put y=vx then given equation becomes 21

1dv vxdx v

by separating variables by apply integrationn then we get

1 2 2tan logy x y cx



29. If 2 2

2 2 1x 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: 1Sol: .diff w.r to ‘x’ on both sides

2

2

dy b xdx a y

again diff w.r to ‘x’ on both sides

2 4

2 2 3

d y bdx a y

30. 2 41

1 2lim1 1y y y

1) 12 2)

13 3)

14 4) 0

Key: 1

Sol: . 2 2 21

1 2lim1 1 1y y y y

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

1) 2

1( ) siny x x Cx

2) 2

1( ) cosy x x Cx

3) 2( ) Cy x xx

4) ( ) Cy x xx

Key: 3

Sol: . 23ydx xdy x dx

2( ) 3d xy x dx

integrating on both sides then we get 2 cy xx

32. If the coefficients of (2 1)thr term and ( 1)thr term in the expansion of 42(1 )x are equalthen r can be1) 12 2) 14 3) 16 4) 20Key: 2Sol: .Given that 2 1 1r rT T then weget r=14

33. A point on the plane that passes through the points (1, 1,6), (0,0,7) and perpendicular to theplane x-2y+z=6 is1) (1, 1, 2) 2) (1,1, 2) 3) ( 1,1, 2) 4) (1,1, 2)Key: 2



Sol: Let the plane passing through poit 1, 1,6 is

1 1 6 0a x b y c z ...........(1)

If this plae pssing through 0,0,7

0a b c ...............(2)If the plane r to the given planeThen 2 0a b c ............(3)From (2) & (3)We get equation of plane is 3 2 7 0x y z By verification (2) option satisifying the plane equation.

34. If the slope of the tangent to the curve 3 4y ax bx at (2,14) is 21, then the values of a andb are respectively1) 2,-3 2) 3,-2 3) -3,-2 4) 2,3Key: 1

Sol: . 23dy ax bdx

slope (m)= 12a+b 12 21a b ........... ( 1) sub point on the curve then weget 4a+b=5 ...........(2) by solving ( 1) and (2) weget a=2,b=-3

35. The probability distribution of a random variable X is given below.x 1 2 3 4 5 6P(X=x) a a a b b 0.3If mean of X is 4.2, then a and b are respectivley equal to1) 0.3,0.2 2) 0.1,0.4 3) 0.1,0.2 4) 0.2,0.1Key: 3Sol: .sum of prbabilities =1

3 2 0.7a b .............( 1)given mean=4.2

2 3 4 5 1.8 4.2a a a b b 6 9 2.4a b ............ (2)

by solving 1 and 2 we get 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 0

5f

2) 2 05

f

3) 3 0

5f

4) 3 05

f

Key: 4Sol: . (0) (1) 0 2 0f f a b c .............(1)

( 2) 0 4 2 0f a b c ........... ( 2) by soving ( 1) and ( 2)

5 7 6a b c



then f(x)= 25 7 6x x

by verification 3 05

f

37. 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 ya b 4)

x y na b

Key: 2

Sol: . diff w.r to ‘x’ on both sides then slope ( m)= ba

then equation of tangent is 1 1( )y y m x x

2x ya b

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

19 4x y

then k=

1) 5

13 2)

135

3) 135

4) 5

13

Key: 2

Sol: Normal condition is 22 22 2

2 2 2

a ba bl m n

by sub the values we get k= 13

5

39. The product of the real roots of 22

8 18 9 0x xx x

is

1) 2 2) 1 3) 3 4) 7Key: 2Sol: .By solving given equation weget

4 3 28 9 8 1 0x x x x

4 1S

40. If

1 5 60 1 70 0 1

and '

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

Sol: . '1, 0 satisfies the second option



41. A village has 10 players. A team of 6 players is to be formed. 5 members are chosen first out ofthes 10 players and then captain is chosen from the remaining players. Then the total numberof ways of cho9osing such teams is

1) 1260 2) 210 3) 610 5!C 4) 510 6CKey: 1Sol: 10 5

5 1 1260C C 42. The equation of the straiht line passing throught the point of intersection of

5 6 1 0,3 2 5 0x y x y and perpendicular to the line 3 5 11 0x y is1) 5 3 18 0x y 2) 5 3 18 0x y 3) 5 3 8 0x y 4) 5 3 8 0x y Key: 3Sol: 5 6 1 0x y

3 2 5 0x y

6 1 5 6

2 5 3 2

130 2 3 25 10 18

x y

1, 1x y

1, 1p

33 5 11 ,5

x y m

51 13

y n

3 3 5 5y x

5 3 8 0x y .

43. An integer is choosen from 2 / 9 10 .k k The probability that it is divisible by both 4 and6 is

1) 1

10 2) 120 3)

14 4)

320

Key: 4

Sol: 18, 16, 14, 12,0,12,14,16,18, 20s

201n s C , the numbers divisible by both 4 and 6 3n E

320

p E .

44. 4 1dx

x 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



Sol: 4

11

dxx x

4

1 31x x

31 1 4

4 1y

xdx dxx x

41cos 14

x x c

4 41 1cos 14 4

x x c

4

4

14 1

xlesx

.

45. 1 13 2sin sin2 3

1) 1 3 2sin2 3

2)

1 3 2sin2 3

3) 1 3 2sin

2 3

4)

1 3 2sin2 3

Key: 2

Sol: 3 2sin sin

2 3

3 2,2 3

x y

2 2 1x y

1 1 1 2 2sin sin sin 1 1x y x y y x

1sin

1 3 2sin2 3

46. and are the roots of 2 2 0.x x C If 3 3 4, then the value of C is1) -2 2) 3 3) 2 4) 4Key: 3

Sol: 3 32, , 4C

33 3 3



4 8 3 2c

4 8 6c 6 12 2c c .

47. 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 0S 2) an internal point with respect to the circle 0S 3) the centre of the circle 0S 4) a point on the circle 0S Key: 2

Sol: Given ole 2 2 13 0x y

Eqn of tangent at 2,3

2 3 13 0x y

slope 2

3m

1 2 3, ,3 2

p mm

11 0s P lies insidethe circle .48. Using the letters of the word TRICK, a five letter word witth distinct letters is formed such

that C is in the middle. Tn how many ways this is possible?1) 6 2) 120 3) 24 4) 72Key: 3

Sol: C

No of ways = 4! = 24.

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

1) 1 1tan

3

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

3

Key: 2

Sol: 2 8 1 8 2x y xy

Solving (1) and (2) we get , 4,2x y

1 2

1 2

tan1m m

m m

1tan 3 .



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

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

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

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

4) 1f doesnot existKey: 1

Sol: . 2f x x

1f x y x f x

2x y y x

1f x x

Domain [0, )

Range ( ,0]

51. 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

Sol: 1a b c

0a b c

0b a b c

,b c a b c a a b

3c b b c c a a b

3 sin3

a b

3 3 33.1.1.2 2

52. 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

Sol: cosx A nt

sindn A nt ndt



2

22 cosd n n A nt

dt

22

2 0d x n xdt

53. If a

and b

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

is a unit bvectorwhen cos

1) 12

2) 12 3)

32

4) 3

2Key: 1

Sol: 1 1a b a b

22 2 . 1a b a b

1 1 2 1a b

12

or .

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

1) 5,1,0 2) 5,0,1 3) 5,3,1 4) 5,1,3Key: 3

Sol: A B

CD

D A C B

4 6 5, 4 5 6, 1 1 1

5,3, 1 .

55. If 2 22 10 2 5 16 3 0x xy y x y represents a pair of straight lines, then point ofintersection of theose lines is

1) 2, 3 2) 5, 16 3) 710,

2

4)

310, ,2

Key: 3

Sol: 0, 0df dfdx dy

10 5 0, 10 2 16 0hx y y xy

7, 10,2

x y

.



56. 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

Sol: 2

1

x x xx x xx x x

2 2 1 3 3 1,R R R R R R

0 1 00 0 1

x x xx x

0x .

57. If the vectors , 2a i j k b i j k and 2c xi x j k

are coplanar, then x=

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

Sol: 0abc

1 1 11 1 2 0

2 1x x

3 2 1 1 2x x

3 2 2 0x x 2 4x

2x .58. 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 shifted is

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

Key: 1

Sol: 2 24 8 10 8 4 14 0x xy y x xy

01 0dy dfdx dy

8 8 8 0 8 20 44 0x y x y

1 0 2 5 11 0x y x y

1& 2 2,3 ,so x y .



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) 3 ,5a a 2) 2 ,a a 3) 5,3aa

4) ,a a

Key: 3

Sol: 1 2 1 22,3 5,6r r a c c

1 2 9 9 18d c c 2 2 2

1 2d r r 2 218 a a

22 18a 2 9a

3a

7 9,2 2

9 712 2

y x

2 9 2 7y x

2 2 16 0x y

8 0x y

By verification 5, ,3ax y a

.

60. 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

Sol: 1 2

1 2

sin coscos sin

k

1 2

2

1 cos ,cossin ,sink

1 2

1 2

cos11 cos

kk

.

61. Let 2 3a i j k and 3 2b i j k

. Then the volume of the parallelopiped having

coterminous edges as a , b and c , where e c is the vector perpendicular to the plane of a , b

and 2c is

1) 2 195 2) 4 3) 200 4) 195Key: 1



Sol: . 2 3a i j k , 3 2b i j k

1 .a b c a b c

= ˆ| | | |cos ,a b c a b c

| | 2 1 3 (11) (7) (5)1 3 2

i j ka b i j k

= 11 7 5i j k

121 49 25 195a b

195 .2.( 1) 2 195a b c

62. The local maximum of 3 23 5y x x is attained at1) x = 0 2) x = 2 3) x = 1 4) x = - 1Key: 1

Sol: 3 23 5y x x

23 6dy x xdx

, 0dydx

23 6 0x x

2

2 6 6d y xdx

3 ( 2) 0x x

0, 2x x

2

20

6 0x

d ydx

,

2

22

12 6 6 0x

d ydx

Local maximum Local minimum

63. In the expansion of (1 )nx , the coefficients of thp and ( 1)thp terms are respectively p and q,then p + q =1) n + 3 2) n + 2 3) n 4) n + 1Key: 4

Sol: (1 )nx1

( 1) 1 1n p

P p pT T C x 1

npC p

1n p

P pT C x npC q

11

n n np p pp q C C C

1n

pn

p

Cpq C

1p pq n p



1q n p

1p q n

64. If

2 2

sin 00 1

( )2 1 2

0 2

x if xx a if x

f xbx if x

if x

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

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

Sol: 0 0( ) ( )

x xLt f x Lt f x

2 2

0 0sin

x xLt x Lt x a

20 0a a

2 2( ) ( )

x xLt f x Lt f x

2 22 (0)

x xLt bx Lt

2 2 0b

1b

0 1 0 1a b ab

65. If 1cosh 2 log 2 1ex , then x =

1) 1 2) 2 3) 4 4) 3Key: 4

Sol: 21cosh log 2 1ex

2log 1 log 3 9 1e ex x

3x

66. For any integer 1n , 1

( 2)n

KK 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

Sol:1

( 2)n

KK K

= 1.3 2.4 3.5 4.6 ....

= ( 1) (2 7)

6n n n

.



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

1) 5 21 , 2

10

2) 5 212,

10

3) 5 21 , 2

10

4) 2 212,

10

Key: 2

Sol: 2 225 4 100 4 100 0x y x y

2 2 125( 4 4) 4 1004

x x y y

100 1

2 125( 2) 4 12

x y

2

21

( 2) 2 11 125 4

yx

1( , ) 2,2

h k

15

a , 12

b a b

Foci = ( , )h k be ,

1 1214 25

1 54

e

= 1 1 212, ,2 2 5

= 5 212,

10

68.

72

1 cos sin12 12

1 cos sin12 12

i

i

1) 0 2) - 1 3) 1 4) 12

Key: 3

Sol:

72

1 cos sin12 12

1 cos sin12 12

i

i



=

722

2

2cos 2sin cos24 24 24

2cos 2sin cos24 24 24

i

i

= 3 6 13

cis ciscis

69. If the range of the function ( ) 3 3f x x is {3, 6, 9, 18} , then which of the followingeements is not in the domain of f ?1) - 1 2) - 2 3) 1 4) 2Key: 1Sol: By verification ‘-1’ is not in the domain.

70. In ΔABC , if a = 1, b = 2, oC 60 then 2 24 c

1) 6 2) 3 3) 3

24) 9

Key: 1

Sol: 1, 2, 60a b C

22 2 2 214 4 sin 2 cos

2b c ab c a b ab c

= 4 1.4

1. 4 3.4

1 4 2.1. 2 1.2

=3 + 3 = 6

71. If the magnitude of a , b and a b

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

is1) 3 2) 4 3) 6 4) 5Key: 4

Sol: | | 3, | | 4,| | 5a b a b

2 2 2 2| | | | 2 | | | |a b a b a b

225 | | 2 9 16a b

= 2| | 25a b

= | | 5a b

72. If 21( )cos ( )2

f x x dx f x C and (0) 0f , then '(0)f

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



Sol: ( ) sin (0) 0f x x f

'( ) cosf x x

'(0) cos 0 1f

73. If and are the roots of the equation 2 0ax bx c and the equation having roots 1

and 1 is 2 0px qx r , then r =

1) a + 2b 2) ab + bc + ca 3) a + b + c 4) abcKey: 3

Sol: 2 0ax bx c , ,b ca a

Put 1 1x x

sub in (1) 1(1 ) 1

1x

x

22 0 (1 ) (1 ) 0

(1 ) 1a b c a b x c xx x

2 ( 2 ) ( ) 0cx b c x a b c

r = a + b + c

74. If 3A

, 6B

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 1 4) 6 3 1

Key: 1

Sol: Length of chord AB = 2 sin2

A Ba

= 2(12)sin(15)

= 2 126 2 3 1.

2

2 6 6 2

75. If the pair of straight lines 1 0xy x y and the line 3 0x ay are concurrent, then the

acute angle between the pair of lines 2 213 7 23 6 0ax xy y x y is

1) 1 5cos

218

2) 1 1cos

10

3) 1 5cos

173

4) 1 1cos

5

Key: 2



Sol: 1 0xy x y , 3 0x ay

( 1) ( 1) 0x y 1 3 0a 2 22 13 7 23 6 0x xy y x y

1 0x

1 0y 2a 15 5cos

81 169

5 10

( , ) (1,1)x y 1 1cos

10

76. The number of solutions of cos 2 sin in (0,2 ) is1) 4 2) 3 3) 2 4) 5Key: 2Sol: cos 2 sin

21 2sin sin 22sin sin 1 0

2sin 1 sin 1 0

1sin2

sin 1

( 1)6

nn ( 1)

2nn

06

n

516

n

2 2 32 2

n

number of solutions = 377. 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: 4Sol: a = 13, b = 14, c = 15

212

a b cs

21.8.7.6 84

4abcR

= 13 4. 15 5

4(8) 6 2

658



84 45 21

r

8 65 4 69R r 78. If A and B are the variances of the 1st ‘n’ even numbers and 1st ‘n’ odd numbers respectively

then1) A = B 2) A > B 3) A < B 4) A = B + 1Key: 1Sol: By simplying A = B

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

1) 5

2 2 2) 7

2 2 3) 9

2 2 4) 1

2 2Key: 3

Sol: 2 8y x .... (1) a = 2

4y x K .... (2) as m = 1

acm

4 2K

12

K

1 ,12

P

from of normal y mx xm am

4 2y x

6 0x y

Perpendicular =

1 1 692

2 2 2

80. If A and B are evens having probabilities, P(A) = 0.6, P(B) = 0.4 and ( ) 0P A B , then theprobability that neither A nor B occurs is

1) 14 2) 1 3)

12 4) 0

Key: 4

Sol: P A B P A B

= 1 P A B

= 1 0.6 0.4 0

= 0



PHYSICS81. 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 is1) 13% 2) 10% 3) 7 % 4) 12 %Key: 2

Sol: 2p F LP F L

4% 2 3%10%

82. A positive charge ‘Q’ is placed on a conductiing spherical shell with inner radius 1R and outer

radius 2R . A particle with charge ‘q’ is placed at the center of the spherical cavity. Themagnitude of the electric field at a point in the cavity, a distance ‘r’ from center is

1) zero 2) 204

QR 3) 2

04q

R 4)

204

q QR

Key: 3

Sol: 20

14

qEr

83. A swimmer wants to cross a 200 m wide river which is flowing at a speed of 2 m/s. The velocityof the swimmer with respect to the river is 1 m/s. How far from the point directly opposite tothe starting point does the seimmer reach the opposite bank?1) 200 m 2) 400 m 3) 600 m 4) 800 mKey: 2Sol:

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 weber to 2weber. The induced current in the circuit is

1) 2 1

5Rnt

2) 2 1

5n

Rnt

3) 2 1

Rnt

4) 2 1

5n

Rt

Key: 2

Sol:

2 1

4n

R R t

85. A Simple pendulum of length 1m is freely suspended from the ceiling of an elevator. The timeperiod of small oscillations as the elevator moves up with an acceleration of 22 /m s is (use

210 /g m s )

1) 5s

2) 25

s 3) 2s

4) 3s

Key: 4

Sol: 2 lFg a



12124

12 3

86. Consider a metal ball of radius ‘r’ moving at a constant velocity ‘v’ in a uniform magneticfield of induction B . Assuming that the direction of velocity forms an angle ‘ ’ with thedirction of B , the 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: 1Sol: . sine r BV

87. Each of the six ideal batteries of emf 20V is connected to an external resistance of 4 asshown in the figure. The current through the resistance is

1) 6 A 2) 3 A 3) 4 A 4) 5 AKey:Sol: Conceptual

88. The energy that should be added to an electron to reduce its de-Broglie wavelenght from 1nm to 0.5 nm is1) four - time the initial energy 2) equal to the inital energy3) two - times the initial energy 4) three - times the inital energyKey: 4

Sol: 2

2 2

12

hE Em

2 22 1

1 2

2 1

0.51

4

EEE E



89. In the given circuit, a charge of 80 C is given to upper plate of a 4 F capacitor. At steadystate the charge on the upper plate of the 3 F capacitor is :

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

Sol: 1

1

80 165

e

e

Q QVC C

1 1 1 16 3 48Q C V C

90. The Young’s modulus of a material is 11 22x10 /N m and its elastic limit is 8 21x10 /N m . For a awire of 1 m length of this material, the maximum elongation achievable is1) 0.2 mm 2) 0.3 mm 3) 0.4 mm 4) 0.5 mmKey: 4

Sol: .F lYA e

8

4

3

1 10.2 10

0.5 10 0.5

F leA y

mm

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 1 kg, the

angle of inclination is 030 and the coeffcient of static friction between the box and the inclinedplane is 0.2, the minimum magnitude of F

is (Use g = 10 2/m s )

1) 0 N, as 030 is less than angle of repose 2) 1N

3) 3.3 N 4) 16.3 NKey: 3

Sol: min sin cosmgF

1 10 1 30.20.2 2 2

50 0.5 0.173250 0.326816.34N



92. A metre scale made of steel reads accurately at 025 C . Suppose in an experiment an accuracyof 0.06 mm in 1m is required, the range of temperature in which the experiment can beperformed with this metre scale is (coefficient of linear expansion of steel is 6 011 10 /x C )

1) 0 019 30C to C 2) 0 025 32C to C 3) 0 018 25C to C 4) 0 018 32C to CKey: 2Sol: l l t

93. Consider a solenoid carrying current supplied by a DC source with a constant emf contaiingiron core inside it. When the core is pulled out of the solenoid, the change in current will1) remain same 2) decrease 3) increase 4) modulateKey: 1Sol: Conceptual

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

1)

21 32 81 32 8

2)

21 34 81 32 8

3) 58 4)

85

Key: 1

Sol:

2

1 2max

min 1 2

I III I I

1 0 0125%4

I I I

2 03 14 2

I I

95. A thermocol box has a total area (including the lid) of 1.0 2m and wall thickness of 3cm. It is

filled with ice at 00 C . If the average temperature outside the box is 030 C throughout theday, the amount of ice that melts in one day is1) 1 kg 2) 2.88 kg 3) 25.92 kg 4) 8.64 kgKey: 4

Sol: 1 2AKm vice

t l

5 2

2

3 10 3 10 186400 3 10

8.64

m

m kg

96. Which of the following is emitted when 23994 Pu decays into 235

92U ?1) Gamma Ray 2) Neutron 3) Electron 4) Alpha particleKey: 4



Sol: 239 235 49294 2

LimitsPu U He

97. An AC generator producing 10 V (rms) at 200 rad/s is connected in series with a 50 resistor,,a 400mH inductor and a 200 F capacitor. The rms voltage across the inductor is1) 2.5 V 2) 3.4 V 3) 6.7 V 4) 10.8 VKey:

Sol: 2 2L CZ x x R

74.33I

10 10 80

74.33 74.33vI v I Lz

98. Wire has resistance of 3.1 at 030 C and 4.5 at 0100 C . The temperature coefficient ofresistance of the wire is1) 0.0012 0 1C 2) 0.0024 0 1C 3) 0.0032 0 1C 4) 0.0064 0 1C

Key:

Sol: 2 1

1 2 1

R RR t t

4.5 3.1 1.4 0.0064

3.1 100 30 3.1 70

99. An object is thrown vertically upward with a speed of 30 m/s. The velocity of theobject half-a-second before it reaches the maximum height id1) 4.9 m/s 2) 9.8 m/s 3) 19.6 m/s 4) 25.1 m/sKey: 1

Sol: .4 30 3.06

9.8U gt t

g 1 3.06 0.5 2.56t

1 30 (2.56) 4.9 / secV u gt m 100. An electron collides with a Hydrogen atom in its ground state and excites it to n = 3 state.

Theenergy given to the Hydrogen atom in this inelastic collision (neglecting the recoil ofHydrogen atom) is1) 10.2 eV 2) 12.1 eV 3) 12.5 eV 4) 13.6 eVKey: 2Sol: . 2 1 13.6 1.5 12.1E E E ev

101. Consider the mition of a particle described by cos , sin .x a t y a t and z t The trajectoryytraced by the particle as a function of time is1) Helix 2) Circular 3) Elliptical 4) Straight lineKey: 2

Sol: 2 2 2 2 2 2 2sin cosx y z a t a t t



102. Consider a reversible engine of efficiency 1/6, when the temperaure of the sink is reduced by062 C , its efficiency gets doubled. The temperature of the source and sink respectively aree

1) 372 K and 310 K 2) 273 K and 300 K 3) 0 099 10C and C 4) 0 0200 37C and CKey: 1

Sol: 2

1

1TnT

2

1

2 1

22

1

1

2

1 716 6

76

1 62 623

372310

TT

T T

T T TT

T kT k

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 raius of curvature 1 m. The position 's , natureand magnification (m)of the image are1) 's = 0.375 m, Virtual, upright, m = 0.25 2) 's = 0.375 m, Real, inverted, m = 0.253) 's = 3.75 m, Virtual, inverted, m = 2.5 4) 's =3.75 m, Real, upright, = 2.5Key: 1

Sol: .1 1 1f u v

1 1 1 8

3v f u

3 0.3758

v m

Magnification 0.375 0.251.5

vmu

104. An office room contains about 2000 moles of air. The change in the internal energy of thismuch air when it is cooled from 034 C to 024 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 x10 J 2) 51.9 x10 J 3) 54.2 x10 J 4) 50.7 x10 JKey: 3Sol: 2Q U Rdt

1

1

1

5

11

14.2 10

U Q nR tnr RU t nR tr

nR tr

J



105. A ball is thrown at a speed of 20 m/s at an angle of 030 with the horizontal. The maximum

height reached by te ball is (use 210 /g m s )1) 2 m 2) 3 m 3) 4 m 4) 5 mKey: 4

Sol: 2 2sin 400 5

2 2 10 4uH

g

106. A horizontal pipeline carrying gasoline has a cross-sectional diameter or 5 mm. If the viscosityand density of the gasoline are 36 x 10 Poise and 720 3/kg m respectively, the velocity afterwhich the flow becomes turbulent is

1) > 1.66 m/s 2) > 3.33 m/s 3) 31.6 x10 /m s 4) > 0.33 m/sKey: 3

Sol: 3

3

6 10720 5 10cv

dt

31.66 10

107. 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 decrease3) Resistance of copper will decrease while that of germanium will increase4) Resistance of copper will increase while that of germanium will decreaseKey: 3

Sol: Cu MetalGe semconduct

Conceptual

108. A beam of light propagating at an angle 1 from a medium 1 throgh 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

11

SinSin

2) 1

12

SinSin

3) 1

12

4) 1

Key: 1

Sol: 2 1 1 1

1 2 2 2

sinsin

u vu v

2

2 11

sin .sin

109. An amplitude modulated signal consists of a message signal of frequency 1 KHz and peakvoltage of 5V, modulating a carrier frequency of 1 MHz and peak voltage of 15V. The correctdescription 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 65 15sin 2 10 sin 2 10t t 4) 6 315 5sin 2 10 sin 2 10t t Key: 2



Sol: . 0 1 sin sinm cAmv w f w tAc

3 6115 1 sin 2 10 sin 2 103

110. Which of the following principles is being used in sonar technology?

1) Newton’s laws of motion 2) Reflection of electromagnetic waves3) Laws of thermodynamics 4) Reflection of ultrasonic wavesKey:Sol: Conceptual

111. A particle of mass M is moving in a horizontal circle of radius R with uniform speed v. When theparticle moves from one point to a diametrically opposite point, its1) momentum does not change 2) momentum changes by 2 Mv

3) kinetic energy changes by 2

4Mv

4) kinetic energy changes by 2Mv

Key:

Sol: 2i fp p Mv Mv Mv

112. A billiard ball of mass ‘M’, moving with velocity ‘ 1v ’ collides with another ball of the samemass but at rest. If the collsion is elastic the angle of divergence after the collision is1) 00 2) 030 3) 090 4) 045Key:Sol: .Conceptual. (Similar may when collides elastically exchange their celocities)

113. A planet of mass ‘m’ moves in an elliptical orbit around an unknown star of mass ‘M’ suchthat its maximum and minimum distances from the star are equal to 1r and 2r respectively..The angular moment 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

2GMrr r r

Key: 3

Sol: 1 2

1 2

2 r rress

r r

L mvr

2GMm rr

1 2

1 2

2GM r rm

r r

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



Sol: mgh mgs

hs

115. A generator with a circular coil of 100 turns of area 2 22x10 m is immersed in a 0.01 T magneticfield and rotated at a frequency of 50 Hz. The maximum emf which is produced during acycle is1) 6.28 V 2) 3.44 V 3) 10 V 4) 1.32 VKey: 1

Sol: 2 2 210 x10 x 2 x10 x100BNAw = 2 x 3.14=6.28

116. A sound wave of frequency ‘v’ Hz initially travels a distance of 1 km in air. Then it getsreflectedinto a water reservoir of depth 600m. The frequency of the wave at the bottom of the reservoir

is 340 / ; 1484 /air waterV m s V m s

1) > v Hz 2) < v Hz 3) v Hz4) 0 (the sound wave gets attenuated by water completely)Key: 3Sol: .n = constant (conceptual)

117. Which of the following staetmentis not true?1) the resistance of an itrinsic semiconductor decreases with increase in temperature2) doping pure Si with trivalent impurities gives p-type semiconductor3) the majority carriers in n-type semiconductors are holes4) a p-n junction can act as a semiconductor diodeKey: 3Sol: . conceptual

118. The decelration of a car traveling on a straight 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 60 km/hr, thedistance the car will travel and the time it take before it stops are

1) 2 1,3 2

m s 2) 3 1,

2 2m s

a a 3) 3 ,2 2a am s

a 4) 2 2,

3m s

a aKey: 4

Sol: dv a vdf

.dv a dtv

.i

f

v

v

dv a dtv

2i

f

v

vv at

122t v

a



dv a vdt

.dv dx a vdx dt

.dv v a vdx

.dv v a dx

0

0 s

ovv dv a ds

32

02

3v

a

119. A current carrying wire in its neighbourhood produces1) electric field 2) electric and magnetic fields3) magnetic field 4) no fieldKey: 3Sol: Conceptual

120. Consider a particle on which constant forces 1 2 3F i j k N and

2 4 5 2F i j k act together

resulting in a displacement from postion 1 20 15r i j cm to

2 7r k

cm. The total work done onthe particle is1) - 0.48 J 2) + 0.48 J 3) - 4.8 J 4) +4.8 JKey:

Sol: 1 2 2 1F F r r

25 3 20 15 7 x10i j K i j K

248x10

0.48

CHEMISTRY121. Which of the following conditions are correct for real solutions showing negative deviation

from Raoult’s law?

1) 0; 0Mix MixG V 2) 0; 0Mix MixH V

3) 0; 0Mix MixH V 4) 0; 0Mix MixH V

Key: 4Sol: Conceptual



122. Nitration of phenyl benzoate yields the product

1) 2)

3) 4)

Key: 2

Sol: . . Phenyl group connected to oxygen becomes activated for electrophilic

substitution reaction due to the presence of lone pair electrons on oxygen ( it is +M effect)

Substitution of 2NO group takes place at para position of this phenyl group.

The product is

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

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

54 4 5 6Xe f d s 3) 3 254 4 6Xe f s 4) 3 2

54 4 5Xe f d


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

1) 3SO 2) 3SeO 3) PoO 4) TeOKey: 3Sol: Polonium is most metallic in the options given

its oxide PoO is more basic125. The element that forms stable compounds in low oxidation state is

1) Mg 2) Al 3) Ga 4) TlKey: 4Sol: Thallium, due to inert pair effect shows stable lower oxidation state.

126. Atomic radius(pm) of Al, Si, N and F respectively is1) 117, 143, 64, 74 2) 143, 117, 74, 64 3) 143, 47, 64, 74 4) 64, 74, 117, 143Key: 2



Sol: Al, Si belong to 3rd period while O, F to second period. The size decreases from left to right ina period. Order of size is Al>Si> O> F..

127. Reaction of calgon with hard water containing 2Ca ions produce

1) 22 6 18Na CaP O 2) 2 4 3Ca PO 3) 3CaCO 4) 4CaSO

Key: 1

Sol: -2 -2+2 +

4 6 18 2 6 18Ca + Na P O Na CaP O +2NaCalgon

128. Which of the following statement is true1) The pressure of a fixed amount of an ideal gas is proportional to its temperature only2) Frequency of collisions increases in proportion to the square root of temperature3) The value of van der Waal’s constant ‘a’ is smaller for ammonia than for nitrogen4) If a gas is expanded at constant temperature, the kinetic energy of the molecules decreasesKey: 1Sol: As per PV= nRT equation, for a given amount of gas P T .

129. Conversion of esters to aldehydes can be accomplished by1) Stephen reduction 2) Rosenmund reduction3) Reduction with lithium aluminium hydride 4) Reduction with diisobutyl aluminium hydrideKey: 4Sol: Diisobutyl aluminium hydride(DIBAL) is a specific reagent to reduce esters to aldehydes.

130. Consider the following electrode processes of a cell,

212

Cl Cl e

MCl e M Cl

If EMF of this cell is 1.140V and 0E value of the cell is 0.55V at 298K, the value of theequilibrium constant of the sparingly soluble salt MCl is in the order of

1010 2) 810 3) 710 4) 1110

Key: 1Sol: MCl e M Cl cathode (Reduction)

212

Cl Cl e Anode (Oxidation)

212

MCl M Cl

The CK of the cell reaction is calculated from nernst equation

0 0.059 logCell cell CE E Kn

0.0591.140 0.55 log1 CK

0.59 0.059 log CK



0.59log 100.059CK

1010CK

SPK is for 212

M Cl MCl M Cl

1010

1 1 1010Sp

C

KK

131. Which of the following is true for spontaneous adsorption of 2H gas without dissociation onsolid surface.1) Process is exothermic and 0S 2) Process is endothermic and 0S 3) Process is exothermic and 0S 4) Process is endothermic and 0S Key: 1Sol: Adsorption of 2H gas on solid surface is exothermic and entropy decreases in the process.

0S

132. Consider the single electrode process 24 4 2H e H catalyzed by platinum blackelectrode in HCl electrolyte. The potential of the electrode is 0.059V Vs.SHE. What is theconcentration of the acid in the hydrogen half cell if the 2H pressure is 1 bar?1) 1 M 2) 10 M 3) 0.1 M 4) 0.01 MKey: 3

Sol: . 0.059logR PE H

0.059 0.059log H

1

log 1

10

H

H M

133. Which of the following elements has the lowest melting point?1) Sn 2) Pb 3) Si 4) GeKey: 1Sol: The melting point order of IVA group elements isC Si Ge Pb Sn

134. The number of complementary hydrogen bond(s) between a guanine and cytosine pair is1) 2 2) 1 3) 4 4) 3Key: 4Sol: The number of hydrogen bonds between adenine and thymine are two(A=T) Where as thenumber of hydrogen bonds between Guanine and cytosine are three

G C

135. Given 0fH for 2 ,g gCO CO and 2 gH O are e 393.5, 110.5 and 1241.8 kJ mol , respectively..

The 01

fH in kJ mol for the reaction 2 22 g g g gCO H CO H O is

1) 524.1 2) - 262.5 3) - 41.7 4) 41.2Key: 4



Sol: 2 2

H H Hr CO H O COH f f f

110.5 241.8 393.5 41.2 136. Which among the following is the strongest acid?

1) HF 2) HCl 3) HBr 4) HIKey: 4Sol: Among hydrogen halides the strongest acid is HI.As the size of halogen increase, bond length increases hence bond energy decreases. HI releases H ions easily..

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

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

Key: NO KEYSol: 2OsF should be given as 2OSF .

2OSF has pyramida/ shape.

138. The bonding in diborane 2 6B H can be described by1) 4 two centre - two electron bonds & 2 three - centre - two electron bonds2) 3 two centre - two electron bonds & 3 three centre - two electron bonds3) 2 two centre - two electron bonds and 4 three centre - two electron bonds4) 4 two centre - two electron bonds and 4 two centre - two electron bondsKey: 1

Sol: Diborane molecular formula is 2 6B H

Diborane has 4 two centered two e bonds and two three centered two electron bonds.139. The monomers of Buna - S rubber are

1) Isoprene and butadiene 2) Butadiene and phenol3) Styrene and butadiene 4) Vinyl chloride and sulphurKey: 3Sol: The monomers present in buna- S rubber are(1) 1, 3- Butadiene(2) styrene

140. 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: 3Sol: Heating a mixture of 2 2&Cu O Cu S will give 2&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 eVKey: 3



Sol: 2

13.6En eVn

2

13.62

eV

13.64

eV

3.4eV .142. Which of the following are the correct representations of a zero order reaction, where A

represents the reactant?

1) a, b, c 2) a, b, d 3) b, c, d 4) a, c, dKey: 2Sol: In zero order R’n

012 2

At

K

143. 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: 4Sol: The correct order of Ionic radius is

2 2Na Li Mg Be

144. Which one of the following statement is correct for 4d 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-complexes formKey: 1

Sol: When 0 pairing energy pairing of electrons takes place

Low- spin complexes are formed145. The reactivity of alkyl bromides.

1) 3 2CH CH Br 2) 3CH CH Br

3CH3) 3CH C Br

3CH

3CH

4) 3CH Br



Key: 1Sol: In dry acetone reaction follows 2SN mechanism

Hence 3CH Br > 3 2CH CH Br >3CH CH Br

3CH> 3CH C Br

3CH

3CH

146. Optically active 3 3 3CH CH CH CH

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) 3 2 2CH CH CH CH 2) 3 3CH CH CH CH

3) 3 2CH CH CH OH

3CH4) 3 2 2CH CH CH OH

Key: 2

Sol: OH

3 2 3CH CH CH CH Fewdropsof acid

Dehydration 3 3CH CH CH CH

147. Commercially available 2 4H SO is 98 gms by weight of 2 4H SO and 2 gms by weight of water..

It’s density is 1.83 g 3cm . Calculate the molality (m) of 2 4H SO (molar mass of 2 4H SO is 98 g1)mol

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

Sol: 1000 98 1000 500

98 2solute

solute solvent

wm mGMW W

148. Cylohexylamine and aniline can be distinguished by1) Hinsberg test 2) Carbylamine test 3) Lassaigne test 4) Azo dye testKey: 4Sol: Cyclohexylamine is not the aromatic amine so do not give azodye test

149. ________ is a potent vasodilator.1) Histamine 2) Serotonin 3) Codeine 4) CimetidineKey: 1Sol: Histamine is a potent vasodilator.

150. Standard Enthalpy (Heat) of formation of liquid water at 025 C is around

22 212g g lH O H O

1) -237 KJ/mol 2) 237 kJ/mol 3) -286 kJ/mol 4) 286 kJ/molKey: 3

Sol: 20 286 /f H o lH kJ mol



151. 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) 3CH

3 2CH CH CH OH 4)

3CH3CH C OH

3CH

Key: 4Sol: Tertiary alcohols are more reactie towards lucas reagent

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 s1) 36 55 24 24 5 482) 48 5 24 36 55 243) 24 24 36 55 48 54) 24 48 36 24 5 55Key: 2Sol: Verify from options

153. Which of the following elements is purified by vapour phase refining?1) Fe 2) Zr 3) Cu 4) AuKey: 2Sol: Zr is easily decomposed in vapour phase,

154. When helium gas is allowed to expand in to vaccum, heating effect is observed. The reason forthis is (Assume He as a non ideal gas)1) He is an inert gas2) The inversion temperature of Helium is very high3) The inversion temperature of Helium is very low4) He has the lowest boiling pointKey: 3Sol: Gases with low inversion temperature gets heated when allowed to expand in vaccum

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

Identify the correct T-X curve for the same mixture.

1) 2) 3) 4)

Key: 1



Sol: Vapour pressure is inversely proportional to boiling point.156. Cyclopentadienyl anion is

1) benzenoid and aromatic 2) non-benzenoid and aromatic3) non-benzenoid and non-aromatic 4) non-benzenoid and anti-aromaticKey: 2

Sol: Cyclopentadienyl anion It is cyclic, planar with 4 2n e There fore aromatic

but structure is not similar to benzene157. Oxidation of cyclohexene in presence of acidic potassioum permanganate leads to

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

Sol:

Cyclohexene

4KMnO / H

Oxidation

COOH

COOH

adipic acid

158. How many emission spectral lines aer possible when hydrogen atom is excited to nth energylevel?

1) 1

2n n

2) 1

2n

3) 1

2n n

4) 2

4n


159. The bond length (pm) of 2 2 2 2, , ,F H Cl and I respectively is1) 144, 74, 199, 267 2) 74,144, 199, 267 3) 74, 267, 199, 144 4) 144.74.267.199Key: 1Sol: Order of bond length is 2 2 2 2H F Cl I

160. The number of tetrahedral and octahedral voids in CCP unit cell are respectively1) 4, 8 2) 8,4 3) 12, 6 4) 6, 12Key: 2Sol: If there are n atoms in a CCP, the number of tetrahedral voids are 2n and octahedral voids aren.

question paper with solutions - sri gayatri

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