instructions to the candidates (read the instructions...

KAB Model EAMCET-2016Engineering

Hall Ticket Number

(To be filled in by the candidate)

Booklet Code: A ______________Signature of the Invigilator

INSTRUCTIONS TO THE CANDIDATES(Read the instructions carefully before Answering)

1. Separate Optical Mark Reader (OMR) Answer Sheet is supplied to you along with Question Paper Booklet. Please read and follow the instructions on the OMR Sheet for marking the responses and also the required data.

2. Candidates should write the Hall Ticket Number only in the space provided on this page and the OMR sheet. Do not write the Hall Ticket Number anywhere else.

3. Immediately on opening the Question Paper Booklet by tearing off the paper seal please check for (i) The same booklet code (A/B/C/D) on each page, (ii) Serial number of the questions (1 – 160), (iii) The number of pages, and (iv) Correct Printing. In case of any defect, please report to the invigilator and ask for replacement with the same booklet code within five minutes from the commencement of the test.

4. Electronic gadgets like Cell Phone, Pager, Calculator, Electronic watches and Mathematical / Log Tables are not permitted into the examination hall.

5. Darken the appropriate circles of 1, 2, 3 or 4 in the OMR sheet corresponding to correct or the most appropriate answer to the concerned question number in the sheet. Darkening of more than one circle against any question automatically gets invalidated.

6. Rough work should be done in the space provided for this purpose in the Question Paper Booklet.

7. Once the candidate enters the Examination Hall, he/she shall not be permitted to leave the Hall till the end of the Examination.

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10. Return the OMR Answer Sheet to the Invigilator before leaving the examination hall. Failure to return the OMR is liable for criminal action. The Question Paper Booklet shall be taken away by the candidate and should be preserved till the declaration of results.

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This booklet consists of 59 Pages for 160 questions +4 Pages of RoughWork + 1 Title page i.e Total 64 pages

E 2016 A

Q

ABooklet No: 15345

Serial No:

KAB Model EAMCET 2016

Rough Work

E2016A 2 Q

A

Time: 3 Hours Marks: 160

Instructions:

(i) Each question carries one mark.

(ii) Choose the correct or most appropriate answer from the given options to the following

questions and darken, with blue/black ball point pen the corresponding digit 1, 2, 3 or 4 in the

circle pertaining to the question number concerned in the OMR Answer Sheet, separately

supplied to you

OMR

MATHEMATICS

1. The projection of the vector ˆ ˆ ˆi 2j k on the vector ˆ ˆ ˆ4i 4j 7k is

ˆ ˆ ˆ4i 4j 7k ˆ ˆ ˆi 2j k

1) 5

519

2) 1

29

3) 9

194)

16

19

2. Period of 4 46cos x 7 sin x is

4 46cos x 7 sin x

1) 2

2) 3)

3

2

4) 2


Rough Work

E2016A 3 Q

A

3. The no. of real solutions of 1 1 2tan x x 1 sin x x 12

is

1 1 2tan x x 1 sin x x 12

1) Zero 0 2) One 1

3) Two 2 4) Infinite

4. If r2r 2r

Z cos i sin , r 0,1, 2,3, 45 5

. Then z0z1z2z3z4=

r2r 2r

Z cos i sin , r 0,1, 2,3, 45 5

z0z1z2z3z4=

1) 1 2) 1

3) 0 4) None of these

5. If the cube roots of unity are 21, , then the roots of the equation 3x 1 8 0 are

1 21, , 3x 1 8 0

1) 1, 1, 1 2) 21, 1 2 1, 2

3) 21, 1 2 ,1 2 4) 21,1 2 ,1 2

6. If x 2 is a common factor of the expression 2x ax b and 2x cx d, then b d

c a

2x ax b 2x cx d, (x – 2) b d

c a

1) –1 2) –2 3) 2 4) 1


Rough Work

E2016A 4 Q

A

7. A root of equation 2 a b ca c b c

x a x b x a b

is

2 a b ca c b c

x a x b x a b

1) c 2) b 3) a 4) a + b + c

8. The equation of lowest degree with rational coefficients having a root 3 i 2 is

3 i 2

1) 4 2x 2x 25 0 2) 4 2x 10x 1 0

3) 4 2x 10x 1 0 4) 4 2x 2x 25 0

9. A speaks truth in 75% of the cases and B in 80% of the cases. The percentage of cases

they are likely to concur with each other in making the same statement is

A, 75% B, 80%

1) 25% 2) 35% 3) 50% 4) 65%

10. Two 8 faced dice (numbered from 1 to 8) are tossed. The probability that the product

of two counts is a square number is.

1) 1

82)

7

323)

3

164)

3

8


Rough Work

E2016A 5 Q

A

11. The coefficient of x9 in the expansion of x 1 x 4 x 9 ..... x 100 is

x 1 x 4 x 9 ..... x 100 x9

1) 325 2) 385 3) 425 4) 385

12. If 2

x 4

x 5x 6

can be expanded in the ascending power of x, then the coefficient of x3

is

2

x 4

x 5x 6

x x3

1) 73

648

2)

73

6483)

71

6484)

71

648

13. If a flag staff of 6mt high placed on the top of a tower throws a shadow 2 3 mt long

on the ground then the angle that the sun S makes with the ground is

2 3 S

1) 45° 2) 30° 3) 75° 4) 60°


Rough Work

E2016A 6 Q

A

14. If a point P moves such that its distance from the point A(1, 1) and the line

x + y + 2 = 0 are equal, then locus of P is

P A(1, 1) x + y + 2 = 0

P 1) Straight line

2) Pair of Straight lines

3) A parabola

4) An ellipse

15. If the axes are rotated through an angle 45° in the positive direction without changing

the origin then the coordinates of the point 2,4 in the old system are

45°

2,4

1) 1 2 2,1 2 2 2) 1 2 2,1 2 2

3) 2 2, 2 4) 2,2

16. The equation of the line common to the pairs of lines 2 2 2mx m 1 xy my 0 and

2 2mx m 1 xy y 0 is 2 2 2mx m 1 xy my 0 2 2mx m 1 xy y 0

1) x y 0 2) x y m 0 3) mx y 0 4) x y 0


Rough Work

E2016A 7 Q

A17. The radius of a circle touching the lines 3x 4y 5 0 and 6x 8y 9 0 is

3x 4y 5 0 6x 8y 9 0

1) 9

202)

19

203)

29

204)

39

20

18. The length of the latus rectum of the parabola 2y 8x 2y 17 0 is

2y 8x 2y 17 0

1) 2 2) 4 3) 8 4) 16

19. The tangent at any point P on the ellipse meets the tangent at the vertices A and A' of

2 2

2 2

x y1

a b at L and M. Then AL.A ' M

2 2

2 2

x y1

a b A A'

P L MAL. A' M=

1) 2a 2) 2b 3) 2 2a b 4) ab

20. If a latus rectum of a hyperbola subtends a right angle at its centre then its eccentricity

is

1) 3 1

2

2)

5 1

2

3)

5 1

2

4)

3 1

2


Rough Work

E2016A 8 Q

A21. If a 1 then

1x x

1x 0x x

a aLt

a a

a > 1

1x x

1x 0x x

a aLt

a a

1) –1 2) 0 3) 1 4) 2

22. 10 10 10

10 10x

x 1 x 2 ..... x 100Lt

x 10

1) 10 2) 100 3) 1010 4) 1000

23. If 2 4 2ny 1 x 1 x 1 x ..... 1 x then x 0

dy

dx

2 4 2ny 1 x 1 x 1 x ..... 1 x x 0

dy

dx

1) 0 2) 1

23) 1 4) 2

24. If 3 5

12 4

cos x cos xdx Asin x Bcosecx Ctan sin x K

sin x sin x

, then A+B–C =

3 5

12 4

cos x cos xdx Asin x Bcosecx Ctan sin x K

sin x sin x

, A+B–C =

1) –7 2) 5 3) 7 4) 9


Rough Work

E2016A 9 Q

A25. Area bounded by the curves y = |x| and y = 4–| x | is ………

y = |x| y = 4–| x |

1) 8 2) 4 3) 12 4) 16

26. 10

0

x x dx .......... (where [ x ] denotes the greatest integer not exceeding x)

10

0

x x dx .......... ([ x ] x )

1) 10 2) 5 3) 20 4) 0

27. The order of the D.E whose solution is given by 5x c1 2 3 4y c c cos x c c e where

1 2 3 4 5c ,c ,c ,c ,c are arbitrary constants=

5x c1 2 3 4y c c cos x c c e 1 2 3 4 5c ,c ,c ,c ,c

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

28. The solution of x y y xe dx e dy 0 is……

x y y xe dx e dy 0

1) 2x 2ye e c 2) 2x 2ye e c 3) x ye e c 4) x ye e c


Rough Work

E2016A 10 Q

A

29. An integrating factor of the equation 2 3

dy 2y 1

dx x x is……

2 3

dy 2y 1

dx x x

1)1 1

x 2) 2x 3)

22 / xe 4) 2

xe

30. In a ABC, if

1 a b

1 c a

1 b c

=0 then (sin2A + sin2B + sin2C) =

ABC 1 a b

1 c a 0

1 b c

(sin2A + sin2B + sin2C) =

1) 1 2) 3 3) 9 4) 3/8


Rough Work

E2016A 11 Q

A

31. Statement (A): If A is a skew symmetric matrix of order 33 then det A = 0

(A): A33 det A = 0

Statement (B): If A is a square matrix then det A = det A' = det (–A1)

(B): A det A = det A' = det (–A1)

1) Both A and B are individually true and B is the correct explanation of A

AB B, A

2) Both true and B is not correct explanation of A

A, B B, A

3) A is true and B is false 4) A is false, B is true

A B A B

32. If

2

2 2

2

cos2x sin x cos4x

sin x cos2x cos x

cos4x cos x cos2x

is expanded in powers of sin x then the constant term in the

expansion is

2

2 2

2

cos2x sin x cos4x

sin x cos2x cos x

cos4x cos x cos2x

sinx

1) 1 2) 2 3) –1 4) –2


Rough Work

E2016A 12 Q

A

33. The vectors a 3i j 2k,b i 3j 4k,c 4i 2 j 6k are along the sides of a

triangle. The length of the median bisecting the vector c is

a 3i j 2k,b i 3j 4k,c 4i 2 j 6k

c

1) 10 2) 8 3) 11 4) 6

34. The equation of the plane through the point (2, 1, 0) and perpendicular to the planes

2x – y – z =5 and x +2y–3z = 5

2x – y – z =5 x +2y–3z = 5

1) x + y + z =3 2) 2x + y – z =5 3) x –y –3z =1 4) 3x – y – z =5

35. If e

uu log tan then tanh .......

4 2 2

If eu log tan4 2

u

tanh .......2

1) tan 2) tan2

3) cot

2

4) tan 2


Rough Work

E2016A 13 Q

A

36. A bag contains 40 tickets numbered 1, 2, 3,…..40, of which four are drawn at random

and arranged in ascending order (t1 < t2 < t3 < t4). Then the probability of t3 being 25 is

(t1 < t2 < t3 < t4) t3 = 25

1) 40

424 15

2 1

C

C C2)

415

91393)

514

91394)

414

9139

37. If 2 4 0, 0b ac a , then the domain of the function

3 2log isy ax a b x b c x c

2 4 0, 0b ac a , 3 2logy ax a b x b c x c

1) 2

bR

a

2) : 12

bR x x

a

3) , 12

bR

a

4) R

38. The system of equations 3 4 3, 2 3 2,6 5 3x y z x y z x y z has atleast

one solution when

3 4 3, 2 3 2,6 5 3x y z x y z x y z

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


Rough Work

E2016A 14 Q

A

39. Ten guests are to be seated in a row of which three are ladies. The ladies insist on

sitting together while two of the gentlemen refuse to take consecutive seats. In how

many ways can the guests be seated?

1) 2399976 2) 21844 3) 630624 4) 181440

40. We are required to form different words using all letters of the word INTEGER. Let

m1 be the number of words in which I and N are never together and m2 be the number

of words which begin with I and end with R, then 1

2

m

m=

INTEGER

I Nm1

IRm2 1

2

m

m=

1) 42 2) 30 3) 6 4) 1

30


Rough Work

E2016A 15 Q

A

41. The remainder when 22016 is divided by 17 is

22016 17

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

42. 22f x x x is discontinuous on

22f x x x

1) Z 2) Z – {0} 3) Z – {1} 4) Z – {0, 1}

43. If 2 22 2 2 0ax hxy by gx fy c then dy

dx=

2 22 2 2 0ax hxy by gx fy c dy

dx=

1) ax hy

hx by

2) ax hy

hx by

3) ax hy g

hx by f

4) ax hy g

hx by f

44. If the rate of decrease of 2

2 52

xx is twice the decrease of x, then x =

2

2 52

xx x x =

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


Rough Work

E2016A 16 Q

A

45. A triangle is inscribed in a semi-circle of radius ‘a’ so that one side is the bounding

diameter. The maximum area of triangle is

‘a’

1) 2

4a

2) 21

2a

3) 21

4a

4) 2a

46.cos sin

dx

x x

1) 1

log tan2 82

xc

2) 1 3

log tan2 82

xc

3) 1 3

log tan2 82

xc

4) 1

log cot22

xc

47. 13log 4 1xe x dx

1) 4log 1x c 2) 41log 1

4x c 3) 4log 1x 4) 41

log 13

x

48.2 2 2 2

1 1...

1 2nLt

n n

=

1) 2) 2 3) 2

4)

3

2


Rough Work

E2016A 17 Q

A

49. The side of a square is of length 4. The centre of the square is (3, 7) and one of its

diagonals is parallel to y = x. Then the coordinates of its vertices are

y = x

1) (1, 5), (1, 9), (5, 9), (5, 5) 2) (2, 5), (2, 7), (4, 7), (4, 4)

3) (2, 5), (2, 6), (3, 5), (3, 6) 4) (0, 0), (2, 1), (1, 2), (5, 6)

50. If the base of an isosceles triangle is of length 2a and the length of the altitude

dropped to the base is h, then the distance from the midpoint of the base to the side of

the triangle is

2ah

1) 2 2

ah

a h 2)

2 2

ah

a h3)

2 2

ah

h a4) 2 2a h

51. If ' ' is the parameter, then the family of lines

2cos 3sin 3cos 5sin 5cos 2sin 0x y pass through the fixed

point

' ' 2cos 3sin 3cos 5sin 5cos 2sin 0x y

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


Rough Work

E2016A 18 Q

A

52. The lengths of the tangents from the points A and B to the circle are 1l and 2l

respectively. If A and B are conjugate points, the AB2 =

A B 1l 2l

ABAB2 =

1) 2 21 2l l 2) 2 2

1 2l l 3) 2 21 2l l 4)

2122

l

l

53. Two circles of radii r and R intersect at an acute angle . The length of their common

chord is

r R

1) 2 2

2 sin

2 cos

rR

r R rR

2)

2 2

2 sinrR

r R

3) 2 2

2 cosrR

R r

4)

2 2

2 cosrR

R r

54. The distance between the circumcentre and the orthocenter of the triangle formed by

(1, 2, 3), (3, –1, 5), (4, 0, –3) is

(1, 2, 3), (3, –1, 5), (4, 0, –3)

1) 1

172

2) 1

662

3) 7

2 4)

17

2


Rough Work

E2016A 19 Q

A55. If 1 1 1 2 2 2, , ; , ,l m n l m n are d.c.’s of two lines then

2 2 2

1 2 2 1 1 2 2 1 1 2 2 1l m l m m n m n n l n l + 2

1 2 1 2 1 2l l m m n n

1 1 1 2 2 2, , ; , ,l m n l m n

2 2 2

1 2 2 1 1 2 2 1 1 2 2 1l m l m m n m n n l n l + 2

1 2 1 2 1 2l l m m n n

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

56. The position vectors of A, B are , a b respectively. The position vector of C is 3

4 2

a b .

Then

A B a b . C 3

4 2

a b

1) C is inside the OAB

C OAB

2) C is outside the triangle OAB but inside the angle AOB

C OAB AOB

3) C is outside the OAB but inside the angle OAB

C OAB OAB

4) Outside of OAB

C OAB

57. If 2 2 , . 14, 3 8a i j k a b a b i j k then b =

2 2 , . 14, 3 8a i j k a b a b i j k b =

1) 5 2i j k 2) 5 5 2i j k 3) 5 5 2i j k 4) 5 5 2i j k


Rough Work

E2016A 20 Q

A

58. Let a be a unit vector, 2b i j k and 3c i k . The maximum value of

[a b c] is

a 2b i j k 3c i k [a b c]

1) –1 2) 10 6 3) 10 6 4) 59

59. In a class of 100 students there are 70 boys whose average marks in a subject are 75.

If the average marks of the complete class is 72, then what is the average mark of the

girls?

1) 73 2) 65 3) 68 4) 74

60. In a Poisson variate X, if P(X = 0) = 0.2 then the variance of the distribution is

X P(X = 0) = 0.2

1) 2 2) 1 3) e 4) loge 5

61. If

1 2 3 4

1 2 3 4

cos cos0

cos cos

, then 1 2 3 4tan tan tan tan

1 2 3 4

1 2 3 4

cos cos0

cos cos

, 1 2 3 4tan tan tan tan

1) 1 2) 2 3) –1 4) –2


Rough Work

E2016A 21 Q

A

62. Minimum value of 27 sec 64 cosx ecx is

27 sec 64 cosx ecx

1) 125 2) 144 3) 225 4) 25

63. In a triangle ABC, let 2

C . If r is the inradius and R is the circumradius of the

triangle ABC, then 2(r + R) =

2C

ABC rR

2(r + R) =

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

64. Mean of 100 observations is 50 and S.D. is 10. If 5 is subtracted from each

observation and then it is divided by 4, then the new mean and S.D. are

1) 11.25, 6.25 2) 11.25, 2.5 3) 11.25, 10 4) 11.35, 3.5

65. Let , ,a b c be three vectors having magnitudes 1, 1, 2 respectively. If 0a a c b

then the angle between a and c is

, ,a b c 0a a c b a c

1) 3

2)

6

3)

4

4)

2


Rough Work

E2016A 22 Q

A

66. The expression

10

1 sin icos10 10

1 sin i cos10 10

is equal to 2where i 1

2i 1

10

1 sin i cos10 10

1 sin i cos10 10

1) 1 2) – 1 3) i 4) –i

67. If the roots of the quadratic equation 2x x 0 are tan30° and tan15°. Then the

value of

2x x 0 tan30° tan15°

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

68. If the distances of the vertices of a triangle ABC from the corresponding points of

contact with the in-circle are 3, 4 and 5 respectively, then the in-radius is equal to

ABC

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

2


Rough Work

E2016A 23 Q

A

69. The most general value of θ which satisfies both equations 1, 1

2 Cos Tan

(where n is an integer) is

1, 1

2 Cos Tan n

θ

1) 3π

2nπ +4

2) π

2nπ +4

3) 5π

2nπ +4

4)7π

2nπ +4

70. Let Q(x) = 1f x f x and '' 0f x for 0 1x . Then, on 1

0,2

Q(x) = 1f x f x '' 0f x , 0 1x . 10,

2

1) Q(x) is increasing Q(x)

2) Q(x) is decreasing Q(x)

3) Q(x) is constant Q(x)

4) Q(x) is not increasing Q(x)

71. The curve 3 2y ax bx cx is inclined at angle 45° to x-axis at (0, 0) but it touches

X-axis at (1, 0) then the value of a, b, c are given by

3 2y ax bx cx X45° X a, b, c

1) a = 2, b = 1, c = 1 2) a = 1, b = –2, c = 1

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


Rough Work

E2016A 24 Q

A

72. A line has intercepts a, b on axes. When the axes are rotated through an angle , the

line makes equal intercepts on axes then tan =

a, b

tan =

1) a b

a b

2) a b

a b

3) a

b

4) b

a

73. If2sin

1 cos siny

then 1 cos sin

1 sin

equals.

2sin

1 cos siny

1 cos sin

1 sin

1) 1 + y 2) y 3) 1 – y 4) 1

y

74. Let f be a function which is continuous and differentiable for all real x. If f (2) = –4

and ' 6f x for all 2,4x , then

xf

f (2) = –4 ' 6,f x 2,4x

1) f (4) < 8 2) f(4) 8 3) f(4) > 12 4) f(4) > 8


Rough Work

E2016A 25 Q

A

75. Let A x : 1 x 1 and f : A A be a function defined by f x x x . then f is:

A x : 1 x 1 f x x x . f : A A f(x)

1) Bijection

2) Surjection but not injection

3) Injection but not surjection

4) None of these

76. Let ‘f’ be a continuous function on [1, 3]. If ‘f’ takes only rational values for ‘x’ and

f(2) =10 then f(1.5) =

[1, 3] ‘f’ ‘f’ ‘x’

f(2) =10 f(1.5) =

1) 8 2) 1 3

2

f 3) 20 4) 10

77. If 2 2 2sin cos 2secA B C then

2 2 2sin cos 2secA B C

1) , ,2

A n B n C n for n z

2) , ,2

A n B n C n for n z

3) ; ,2 2

A n B n C n for n z

4) , ,2

A n B n C n for n z


Rough Work

E2016A 26 Q

A

78. If cos cos 2 cos 3cos

,x x xx

a b c d

then

a c

b d

is equal to

cos cos 2 cos 3cos,

x x xx

a b c d

a c

b d

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

79. If A lies in the third quadrant and 3tan 4 0,A then 5sin 2 3sin 4cosA A A is equal

to

A 3tan 4 0,A 5sin 2 3sin 4cosA A A

1) 0 2) 24

5 3)

24

54)

48

5

80) For all complexes Z1, Z2 Where |Z1| =12 and |Z2 – 3–4i| = 5, the minimum value of

|Z1 – Z2|=

|Z1| =12, |Z2 – 3–4i| = 5 Z1, Z2 |Z1 – Z2|

1) 0 2) 2 3) 7 4) 17


Rough Work

E2016A 27 Q

A

PHYSICS

81. If the unit of length is halved, the unit of time is doubled and the unit of force is halved, then

the unit of power in the new system becomes.

1) 1

2 2)

1

4 3)

1

8 4) 2

82. A bullet moving with a velocity of 1800ms passes through two plates of widths 1 2d and d .

In passing through each of them, it loses a velocity of 1200 ms . If both the plates offer same

resistance to the motion of bullet, then the ratio 1 2d / d is

2d 1d ,

1 2d / d ?

1) 7

52)

5

73)

4

34)

3

4


Rough Work

E2016A 28 Q

A83. The displacements of a particle as a function of time ‘t’ is shown in figure. The figures

indicates,

1) the velocity of the particle is constant throughout.

2) the particle starts with certain velocity, but the motion is retarded and finally the particle

stops.

3) the particle starts with a constant velocity, the motion is accelerated and finally the particle

moves with another constant velocity.

4) the acceleration of the particle is constant throughout.

84. A body is projected from ground with a velocity 140 2ms at an angle 45° to horizontal.

After four seconds, it is stopped and again projected horizontally with a speed 40 ms-1. Its

horizontal displacement from point of its first projection till it strikes ground may be

40 2

1) 400 m 2) 394 m 3) 344m 4) 294 m


Rough Work

E2016A 29 Q

A85. The magnification produced by an astronomical telescope for normal adjustment is 10 and

the length of the telescope is 1.1m. The magnification when the image is formed at least

distance of distinct vision is

1) 18 2) 6 3) 16 4) 14

86. A smooth sphere ‘A’ of mass ‘m’ moving with a constant speed ‘V’ on the smooth horizontal

surface collides elastically with an identical sphere at ‘B’ at rest. After elastic collision, if the

speed of sphere ‘A’ is V/2, then the speed of sphere of ‘B’ is.

‘m’‘A’‘V’

(B)

‘A’ V/2 B’

…….

1) V

22) 3V

23) 3V

24) 5V

2

87. A 10 kg stone is suspended with a rope of breaking strength 30 kg-wt. The minimum time in

which the stone can be raised vertically through a height 10 m starting from rest is

(Take g = 10 N/kg)

breaking strength30 kg.wt

(g = 10 N/kg)

1) 0.5 s ( 2) 1 s ( 3) 2 / 3s ( 4) 2 s (


Rough Work

E2016A 30 Q

A

88. A pendulum is hanging from the ceiling of a cage. If the cage moves vertically up with a

constant acceleration a, its tension is 1T . If it moves vertically down with the same

acceleration a, then the tension is 2T . If the cage moves horizontally with the same

acceleration a, then the tension is T. Now, 22T is equal to

‘a’

2T .

T 22T

1) 2 21 2T T 2) 2 2

1 2T T 3) 2 21 22T T 4) 2 2

1 2T 2T

89. A light rod is pivoted at one end so that it can swing freely in vertical plane as a pendulum.

Two point masses 2m and m are attached to it at distances b and 3b respectively from the

pivot. The rod is held horizontal and then released. The angular acceleration of the system at

the instant it is released is

’b’, ‘3b’m 2m

1) 3

4

mg

b2)

g

b3)

5

11

g

b4)

11

5

g

b

1T .


Rough Work

E2016A 31 Q

A90. An open-topped rail road car of mass M kg has an initial velocity V m/s along a straight

horizontal smooth track. The velocity V remains constant until, at time t = 0, it suddenly

starts to rain. The rain drops fall vertically with a velocity Vy and add a mass 1kg s of water

to the car. The velocity of the car t seconds after the rain starts, assuming that it has not filled

up with water is

M kg V m/s t = 0, Vy t

1) 2Mv

M t 2)

3Mv

M t 3)

Mv

2 M t4)

Mv

M t

91. A child sits stationary at the left end of a long trolley moving uniformly with a speed V on a

smooth horizontal floor. If the child gets up and runs towards the right end of the trolley, the

speed of the CM of the (trolley + child) system is

V

1) < V 2) > V

3) Remains unchanged 4) child

trolley

mV V

m


Rough Work

E2016A 32 Q

A

92. A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of

length L and height h. The speed of its centre of mass when the cylinder reaches the bottom

of the inclined plane is

hl MR

1) 2gh 2) 3

gh4

3) 4

gh3

4) 4gh

93. A 30°, 60°, 90° triangular setsquare of negligible mass is suspended freely from the right

angled corner and weights are hung at the two corners as shown in figure. The ratio of

masses, 1 2m : m of the weights, if the hypotenuse of the set square sets horizontally, is 90°

90°

1m

2m

1 2m : m

1) 3 : 1 2) 1 : 3

3) 1: 3 4) 3 :1

94. The maximum acceleration and time period of a simple harmonic oscillator are 5.0 m/s2 and

6.28s. Its acceleration when the velocity becomes 4ms–1 is

1) 3 m/s2 2) 4 m/s2 3) 2 m/s2 4) 3.14 m/s2


Rough Work

E2016A 33 Q

A95. A metal piece of mass 120 gm is stretched into a thin plane rectangular sheet of area of cross-

section 0.54 m2. If the length and breadth of this sheet are in the ratio 1 : 6, the moment of

inertia about an axis passing through its centre and perpendicular to its plane is

1) 3.3 kg m2 2) 2 23.3 10 kg m 3) 2 26.6 10 kg m 4) 6.6 kg m2

96. Two uniform rods A and B made of materials of thermal conductivity in the ratio 5 : 3 and of

equal length and equal cross sectional areas are joined in series. If the free end of rod A is at

100oC and the free end of rod B is 20oC, the temperature at the junction of two rods will be

A,BA100oCB20oCA,B

1) 50oC 2) 70oC 3) 85oC 4) 90oC

97. The speed of flow of water through a long cylindrical pipe of diameter 2cm so that flow

becomes turbulent is, (Assume that, co-efficient of viscosity 31 10 . ,aP s Reynold’s

number = 3000 and density of water = 103 kg/m3)

31 10 . ,aP s

103 kg/m3)

1) 1.5 m/s 2) 0.15 m/s 3) 2 m/s 4) 1 m/s


Rough Work

E2016A 34 Q

A

98. Kepler’s third law of planetary motion when stated for circular orbits has the form

(V = orbital velocity of a planet and R = distance of the planet from the sun)

V= R =

1) V R 2) 2 1V

R 3)

1V

R 4) 3

2

1V

R

99. On a frictionless horizontal table, a uniform stick is pivoted at

its middle, and a ball collides elastically with one end, as

shown in the fig. During the collision, the quantities that are

conserved in the stick-plus-ball system are (L is angular

momentum, E is energy, P is linear momentum).

L E P

1) L around the pivot. L.

2) L around the pivot and E. L E.

3) L around the pivot P and E. L; P E.

4) L around the pivot, and P. ‘P’L.

100. The volume of air increases by 2% in its adiabatic expansion. The percentage decrease in the

pressure of air is

1) 5.6 2) 2.8 3) 4 4) 6

P


Rough Work

E2016A 35 Q

A

B

C

1k

2k

3k

m

A

101. Pressure versus temperature graph of an ideal gas is as shown in figure. If the density of the

gas at point A is 0 , then density at point B will be

A

0 B

1) 03

4

2) 03

2

3) 04

3

4) 02

102. Refer to the system shown in figure. The elastic potential energies stored in the springs A, B

and C are respectively,

A, B, C

1) 2 2 2 2 2 2

1 2 3

m g m g m g, ,

2k 2k 2k

2) 1 2 3

mg mg mg, ,

2k 2k 2k

3) 1 2 3mgk ,mgk ,mgk

4) 3 1 2mgk ,mgk ,mgk

P

B

A

0T 02TT

03P

0P


Rough Work

E2016A 36 Q

A103. Statement 1: Newton’s equation for speed of sound waves propagating in atmospheric air was

found wrong because, he assumed the process as isothermal.

S1

Statement 2: When sound waves propagate in atmospheric air, the compressions and

rarefactions happen so rapidly that there is not enough time for heat to be distributed in air.

Therefore process is adiabatic.

S2

1) Statement 1 is true, Statement 2 is false S1S2 2) Statement 1 is false, Statement 2 is true S1 S2

3) Statement 1 is true, Statement 2 is true and statement 2 is a correct explanation for Statement 1

S1 S2 S2, S1

4) Statement 1 is true, Statement 2 is true but Statement 2 is not a correct explanation for

Statement 1

S2, S1

104. A car sounding a horn of frequency 1000 Hz passes an observer. The ratio of frequencies of the

horn noted by the observer before and after passing of car is 11:9. If the speed of sound is V,

then the speed of the car would be

1000 Hz

‘V’

1) V 2) 2V 3) V

54)

V

10


Rough Work

E2016A 37 Q

A

105. Three processes compose a thermodynamic cycle shown in the accompanying P – V diagrams

of an ideal gas

P – V

Process 1 2 takes place at constant temperature. During this process 60 J of heat enters the

system.

Process 2 3 takes place at constant volume. During this process 40J of heat leaves the

system.

Process 3 1 is adiabatic.

60 J

40J

The change in internal energy of the system during process 3 1is

1) – 40 J 2) – 20 J 3) + 20 J 4) + 40 J

P

V

1

2

3


Rough Work

E2016A 38 Q

A

106. The force of attraction between two point charges separated by certain distance in air is F1. If

the space between the charges is completely filled with a medium of dielectric constant 4, the

force became F2. If only half of the distance between the charges is filled with the above

dielectric, the force becomes F3. The ratio F1:F2:F3 is

F1F2

F3

F1: F2: F3 =

1) 16:9:4 2) 9:36:16 3) 4:1:12 4) 36:9:16

107. In a parallel-plane capacitor, the region between the plates is completely filled by a dielectric

slab. The capacitor is charged from a battery and then disconnected from it. The dielectric slab

is now taken out. Then

1) The potential difference across the capacitor is reduced

2) The potential difference across the capacitor is increased

3) The energy stored in the capacitor is reduced

4) No work is done by an external agent in taking the slab out


Rough Work

E2016A 39 Q

A

108. The effective resistance between points P and Q of the electrical circuit shown in the figure is

P, Q

1) 2Rr / R r

2) 8R R r / 3R r

3) 2r / 4R

4) 5R / 2 2r

109. A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b

respectively. When a current I passes through the coil, the magnetic field at the centre is

Na

b. I

1) 0NI

b

2) 02 NI

a

3)

0NI bln

2 b a a

4) 0NI a

ln2 b a b


Rough Work

E2016A 40 Q

A110. A conducting wire of mass m and length l slides down with constant speed two smooth

conducting bars, set at an angle to the horizontal as shown in figure. The separation between

the bars is equal to l. The system is located in a uniform magnetic field at induction B,

perpendicular to the plane of the sliding wire and bars. The velocity of the wire is

m l

θ

l

B,

1) 2 2

mgR sin

B l

2) 3

mgR sin

Bl

3) 2 5

mgR

B l

4) 4

mgR sin

Bl

111. Alternating current cannot be measured by D.C. ammeter because

D.C. A.C

1) A.C cannot pass through D.C. ammeter

D.C.

2) A.C. changes direction

A.C.

3) Average value of current for complete cycle is zero

4) D.C. ammeter will get damaged

D.C.


Rough Work

E2016A 41 Q

A112. A clear transparent glass sphere 1.5 of radius R is immersed in a liquid of refractive

index 1.25 A parallel beam of light incident on it will converge to a point. The distance of this

point from the centre will be

R 1.5 ,

1) 3R

7

2) 3R

7

3) R

7

4) R

7

113. In Young’s double slit experiment, the intensity at a point where the path difference is λ/6 (λ

being the wavelength of the light used) is I. If I0 denotes the maximum intensity, then0

I

Iis

equal to λ/6

λ

I 0I 0

I

I

1) 1

22) 3

23) 3

44) 1

4

114. 0.01H inductor and 3 ohm resistance are connected in series with a 220V, 50 Hz A.C.

source. The phase difference between the current and e.m.f in the circuit is

200V, 50Hz 0.01H 3 e.m.f (Phase difference

1) rad2

2) rad

6

3) rad

3

4) rad

4


Rough Work

E2016A 42 Q

A

115. The maximum distance between the transmitting and receiving TV towers is 72 km. If the ratio

of the heights of the TV transmitting tower to receiving tower is 16 : 25, the heights of the

transmitting and receiving towers are

1) 51.2m, 80m 2) 40m, 80m 3) 80m, 125m 4) 25m, 75m

116. In the study of transistor as amplifier, if C

E

I

I and C

B

I

I , where C B EI , I and I are the

collector, base and emitter currents, then

C

E

I,

I C

B

I

I , (IC, IB, IE

1) 1

2) 1

3) 1

4)

1

117. The minimum number of NAND gates required to form NOT, OR and AND gates respectively

are NOT, OR, AND NAND

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


Rough Work

E2016A 43 Q

A

118. Statement 1: In a two input NAND gate if one of the inputs is kept high, it acts as an inverter

Statement 2: A low input produces a high output in NAND gate

S1NAND

S2NAND

1) Statement 1 is true, Statement 2 is false S1 S2

2) Statement 1 is false, Statement 2 is true S1S2

3) Statement 1 is true, Statement 2 is true and statement 2 is a correct explanation for Statement 1

S2 S1

4) Statement 1 is true, Statement 2 is true but Statement 2 is not a correct explanation for

Statement 1’

S2 S1

119. Energy is stored in the choke coil in the form of

1) Heat

2) Electric energy

3) Magnetic energy

4) Electro-magnetic energy


Rough Work

E2016A 44 Q

A

120. An air bubble of volume 1.0cm3 rises from the bottom of a lake 40 m deep at a temperature of

12°C. The final volume of the bubble (atmospheric pressure is equivalent to 10m high water

column) when it reaches the surface of the lake, where water temperature 35°C will be

C

C

1) 6 310.6 10 m 2) 6 35.3 10 m 3) 6 32.8 10 m 4) 6 315.6 10 m

CHEMISTRY

121) In Williamson’s synthesis of ethers, which one of the following is not used?

1) Ethyl bromide

2) Tert butylchloride

3) Sodium Ethoxide

4) Sodium tert butoxide


Rough Work

E2016A 45 Q

A

122) Compounds X and Y give effervescence with NaHCO3 solution, X gives a silver

mirror with ammonical AgNO3, while Y gives a sweet smelling compound on heating

with alcohol in the presence of H2SO4; X and Y are

XYNaHCO3

X AgNO3

YH2SO4

XY

1) HCOOH and CH3COOH 2) CH3CHO and CH3COOH

3) CH3COOH and CH3COCH3 4) CH3COCH3 and HCOOH

123) 3 2

3

1)2 2)

.Ca OHCH MgCl Drydistillation

H OCO A B C In this sequence ‘C’ is …

3 2

3

1)2 2)

.Ca OHCH MgCl Drydistillation

H OCO A B C ‘C’

1) Chloroform 2) Acetaldehyde

3) Acetone 4) Acetic acid


Rough Work

E2016A 46 Q

A

124) The major product of nitration of 6 5 6 5||O

C H C O C H with conc. 3 2 4/HNO H SO mixture is:

6 5 6 5||O

C H C O C H

1) 2)

3) 4)

125) 2 4

4

/3 3 .H KMnO H

Pd BaSOCH C C CH P Q

Here Q is

2 4

4

/3 3 .H KMnO H

Pd BaSOCH C C CH P Q

Q

1) Alkane 2) Alkene

3) Aldehyde 4) Carboxylic acid

126) The percentage of vacant space in ccp and bcc arrangements respectively are ….

ccpbcc

1) 26, 32 2) 26, 26 3) 32, 26 4) 26, 48

3 2 4/HNO H SO


Rough Work

E2016A 47 Q

A

127) The orbital angular momentum for an electron is given by 1 / 2l l h .

The angular momentum for an electron in s-orbital is

1 / 2l l h

‘s’

1) 2

h

2) 2

2

h

3) 1 (One) 4) Zero

128) The species having a pyramidal shape is:

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

129) The velocity of electron is 6 12.2 10 sec . m If the uncertainty in its velocity is 0.1% the

uncertainty in its position is

6 12.2 10 sec . m 0.1%

1) 102.63 10 m 2) 26.3A 3) 26.3 nm 4) 2.63nm

130) Which of the following has largest bond angle?

1) 2NO 2) 2NO 3) 3NO 4) 2NO


Rough Work

E2016A 48 Q

A131) Match the following

List – I I List – II II

A) N i I) Van Arkel

B) ,Ti Zr II) Mond’s Process

C) , ,Si Ge Ga III) Cupellation

D) Ag IV) Zone Refining

A B C D

1) IV III II I

2) I IV II III

3) II I IV III

4) I II III IV

132) 29.5 mg. of an organic compound containing nitrogen was digested according to

Kjeldahl’s method and the evolved NH3 gas was absorbed in 20 mL of 0.1M HCl

solution. The excess of acid required 15 mL of 0.1M NaOH solution for complete

neutralization. The percentage of nitrogen in the compound is:

NH30.1 M HCl

0.1 M NaOH

1) 29.5 2) 59.0 3) 47.4 4) 23.7


Rough Work

E2016A 49 Q

A

133) If the half life of the first order reaction 5 23 gPCl g PCl Cl g is 10 minutes.

The time taken for the decrease in concentration of 5PCl to 10% of the original

concentration is

5 23 gPCl g PCl Cl g

5PCl 10%

1) 30.10 min 2) 23.03 min 3) 69.30 min 4) 33.22 min

134) Assertion (A): O-Toluic Acid is stronger than Benzoic Acid

(A)

Reason (R): CH3 group is a +I group.

(R)CH3 +I

1) Both ‘A’ and ‘R’ are true and ‘R’ is correct explanation of ‘A’.

‘A’‘R’‘R’ ‘A’

2) Both ‘A’ and ‘R’ are true and ‘R’ is not correct explanation of ‘A’.

‘A’‘R’‘R’‘A’

3) ‘A’ is true but ‘R’ is false ‘A’‘R’

4) ‘A’ is false but ‘R’ is true ‘A’‘R’


Rough Work

E2016A 50 Q

A

135) For the equilibrium A B C D , the reaction was studied by using the initial

concentration of ‘A’ as twice that of ‘B’. At equilibrium, the concentration of ‘C’ was

found to be three times that of ‘B’. Then its equilibrium constant, KC is

A B C D ‘A’ ‘B’

‘C’ ‘B’ KC

1) 9 2) 4.5 3) 0.9 4) 1.8

136) Compound ‘A’ with formula C3H6O forms phenylhydrazone with phenylhydrazine

and gives negative Tollen’s test. Compound ‘A’ on reduction gives propane. Then

compound ‘A’ is

C3H6O‘A’

‘A’

‘A’

1) 3 2CH CH CHO 2) 2 3CH = CH OH CH

3) 3 3CH COCH 4) 2CH = CH - CHOH

137)

Here ‘X’ is ‘X’

1) 2) 3) 4)


Rough Work

E2016A 51 Q

A138) Arrange the following in the correct order of their basic character in aqueous medium

I) 3NH II) 3 2CH NH III) 3 2CH NH IV) 3 3

CH N

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

139) In O2–, O2 and O2

2– species, the total number of antibonding electrons are respectively.

O2–, O2 O2

2– (antibonding electrons)

1) 7, 6 and 8 2) 1, 0 and 2 3) 6, 6 and 6 4) 8, 6 and 8

140) In the reaction0

2 2NaNO HC ,O C H O, warm6 5 2C H NH X Y,l Y is

2 2NaNO HC ,O°C H O, warm6 5 2C H NH X Yl ‘Y’

1) 6 5C H Cl 2) 6 6C H 3) 6 5C H OH 4) 6 5C H CHO

141) The complex showing a spin only magnetic moment of 2.82 B.M is….?

2.82 B.M

1) 4

Ni CO 2) 2

4NiCl

3) 3 4Ni Pph 4)

2

4Ni CN


Rough Work

E2016A 52 Q

A142) Partial pressure of methane gas is the highest in which among the following mixtures

at STP.

STP

1) Equimolar mixture of methane and SO2

SO2

2) Equimolar mixture of methane and He

He

3) Mixture of CH4 and SO2 of equal weights

SO2

4) Mixture of CH4 and He of equal weights

He

143) The solubility product of Mg(OH)2 is 121.0 10 at 25°C. Aqueous NaOH solution is

added to a 0.01M aqueous solution of MgCl2. The minimum pH at which precipitation

occurs at 25°C is

25°C Mg(OH)2 1.0×10–12. 0.01M MgCl2

25°C NaOH pH

1) 10 2) 5 3) 6 4) 9.0


Rough Work

E2016A 53 Q

A

144) For the reaction 1, 7.5A B H KJ mol and 1 125S JK mol . The value of G and

the temperature, at which the reaction reaches equilibrium are respectively.

1, 7.5A B H KJ mol 1 125S JK mol

G T

1) 0 1KJ mol and 400 K 2) –2.5 1KJ mol and 400 K

3) 2.5KJ mol and 200 K 4) 0 1 300KJ mol and K

145) Choose the correct statement

1) Lyophilic sols can be coagulated by adding excess of electrolyte

2) Viscosity of lyophilic sol. is less than that of dispersion medium

3) Higher the gold number of lyophilic sol. more is its protective power

4) Gases with higher critical temperature will adsorb less


Rough Work

E2016A 54 Q

A

146) XeF6 on hydrolyses to give an oxide. The structures of XeF6 and the oxide,

respectively, are-

XeF6 XeF6

1) Octahedral and tetrahedral 2) Distorted octahedral and pyramidal

3) Octahedral and pyramidal 4) Distorted octahedral and tetrahedral

147) When MnO4– oxidizes separately (i) oxalate ion in acidic medium & (ii) HCl. The

ratios of 24 2 4:MnO C O in (i) and 4 :MnO HCl in (ii), in the respective balanced

chemical equations are respectively

24 2 4:MnO C O (i)

(ii) HCl

(i) MnO4–: C2O4

2– 4 :MnO HCl

1) 1:5 and 2:5 2) 2:5 and 1: 8 3) 2:5 and 1:5 4) 5:2 and 1:8


Rough Work

E2016A 55 Q

A

148) Which of the following statement(s) are correct?

(i) More number of oxidation states are exhibited by the actinoids than those by the

lanthanoids due to lesser energy difference between 5f – and 6d – in actinoids than 4f

– and 5d – orbitals in lanthanoids.

5f 6d 4f 5d

(ii) There is a gradual decrease in the radii of the trivalent ions with the increasing

atomic number in the lanthanoids series.

(iii) The 5f-orbitals are deeply seated than the 4f-orbitals in the atom.

5f 4f

(iv) Zr and Hf have about the same radius due to lanthanoid contraction

Zr Hf

1) (i), (ii), (iv) 2) (i), (ii), (iii) 3) (i), (ii) 4) (i), (ii), (iii), (iv)


Rough Work

E2016A 56 Q

A

149) Which of these compounds is formed in an aldol condensation?

1) 2)

3) 4)

150) Consider the following statements:

I) Monosaccharide’s are optically active polyhydroxy carbonyl compounds.

II) Fructose does not reduce Fehling’s solution.

III) -D (+) - glucopyranose and -D (+) - glucopyranose are anomers.

-D (+) -D (+)

IV) D-glucose and D-mannose are C-2 epimers.

D- D- C-2

Which of the given statements are correct?

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


Rough Work

E2016A 57 Q

A

151) Which one is not correct statement regarding green house effect?

1) It is due to high concentration of CO2 in atmosphere

CO2

2) It is influenced by gases such as CH4, O3 and CFC

CH4, O3 CFC

3) It would result in the warming up of the earth

4) It would result in lowering the level of oceans due to high evaporation

152) A mixture of BCl3 and hydrogen is subjected to silent electric discharge to form “A”

and HCl. “A” is mixed with NH3 and heated at 200°C to form “B”. The formula of

“B” is.

BCl3 H2 “A” HCl

“A” 200°C “B” “B”

1) H3BO3 2) B2O3 3) B3N3H6 4) B2H6


Rough Work

E2016A 58 Q

A153) In which of the following arrangements, the order is not correct according to the

property indicated against it?

1) O2– > F– > Na+ > Mg2+ > Al3+ (ionic radii)

O2– > F– > Na+ > Mg2+ > Al3+

2) F < Cl > Br > I (Electron gain enthalpy)

F < Cl > Br > I

3) B < C < O < N (First ionization enthalpy)

B < C < O < N

4) SiO2 > P2O5 > SO3 > Cl2O7 (acidic nature)

SiO2 > P2O5 > SO3 > Cl2O7

154) In 0.2 molal aqueous solution of a weak acid HX the degree of ionization is 0.3.

Taking kf for water is 1.85 K–Kg–Mol–1, the freezing point of the solution will be….

0.2 HX kf

1.85 K–Kg–Mol–1

1) – 0.260°C 2) +0.480°C 3) –0.480°C 4) –0.360°C


Rough Work

E2016A 59 Q

A155) Which of the following is an example of a broad spectrum antibiotic?

1) Penicillin G G 2) Chloramphenicol

3) Streptomycin 4) Ampicillin

156) Coloured & Paramagnetic gas which can undergo dimerization easily is,

1) NO 2) NO2 3) ClO2 4) SO2

157) Choose the incorrect statement.

1) Magnesium does not give flame colour

2) Potassium is lighter than sodium

3) Solubility: NaHCO3 > KHCO3

4) mp: Li > Na > Kb > Rb > Cs

158) Which one of the following is not a condensation polymer?

1) Terylene 2) Bakelite

3) Nylon-6 4) Polyvinyl chloride


Rough Work

E2016A 60 Q

A159) On electrolysis of 50% 2 4H SO solution in cold condition, the product formed at

cathode is

50% 2 4H SO

1) 2H 2) 2 2H O 3) 2 2 8H S O 4) 2 5H SO

160) The main product of the following reaction is

2 4.6 5 2 3 2

conc H SOC H CH CH OH CH CH

1) 2)

3) 4)


Rough Work

E2016A 61 Q

A


Rough Work

E2016A 62 Q

A


Rough Work

E2016A 63 Q

A


Rough Work

E2016A 64 Q

A

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