CUSAT CAT 2017 Question Paper B.Tech

(x − b)(x − c) (x − c)(x − a) (x − a)(x − b)
1. If P (x) = + + , then for all real
(a − b)(a − c) (b − c)(b − a) (c − a)(c − b)
values of x , P (x) equals

(A) 1 (B) 0
(x − a)(x − b)(x − c)
(C) x (D)
(a − b)(b − c)(c − a)

2. Solution of 0 < |3x + 1| < 31 is

(A) (−4/9, −2/9) (B) [−4/9, −2/9]
(C) (−4/9, −2/9) − {−1/3} (D) [−4/9, −2/9] − {−1/3}

3. If x + x1 = a, x3 + x13 = b , then x2 + x12 is

(A) a3 + a2 − 3a − 2 − b (B) a3 − a2 − 3a + 4 − b
(C) a3 − a2 + 3a − 6 − b (D) a3 + a2 − 3a + 4 + b

4. Two distinct polynomial f (x) and g(x) are defined by f (x) = x2 + ax + 2
and g(x) = x2 + 2x + a . If the equations f (x) = 0 and g(x) = 0 have a
common root, then the sum of the roots of the equation f (x) + g(x) = 0 is
(A) − 12 (B) 0
(C) 12 (D) 1

2 2
5. 4sin x + 4cos x is

(A) ≤ 4 (B) ≥ 4
(C) ≤ 2 (D) ≥ 2

6. Let A(2,-1) and B(6,5) are two points. The ratio in which the foot of the
perpendicular from (4,1) divides AB is

(A) 8 : 15 (B) 5 : 8
(C) -5 : 8 (D) -8 : 5
1

7. Solution of |x − 1| + |x − 2| + |x − 3| ≥ 6 is

(A) [0, 4] (B) (−∞, −2) ∪ [4, ∞)
(C) (0, 4). (D) (−∞, 0) ∪ [4, ∞)

8. A man standing on a railway platform notices a train moving at uniform speed
took 21 seconds to cross the platform which is 88 meters long and that it took
9 seconds to pass him. Then the length of the train in meters is

(A) 55 (B) 160
(C) 66 (D) 72

9. The largest non-negative integer k such that 24k divides 13! is

(A) 2 (B) 3
(C) 4 (D) 5

10. If the three points A(1, 6), B(3, −4) and C(x, y) are collinear then the equa-
tion satisfying by x and y is

(A) 5x + y − 11 = 0 (B) 5x + 13y + 5 = 0
(C) 5x − 13y + 5 = 0 (D) 13x − 5y + 5 = 0

11. The number of solutions of 2 sin x + cos x = 3 is

(A) 1 (B) 3
(C) infinite (D) 0

12. The period of the function f (x) = cos 4x + tan 3x is

(A) π (B) π2
(C) π3 (D) ∞

2

13. From a circular disk of radius 13 cm a sector is cut with center angle θ . If
the height of the right circular cone formed using the above sector is 12 cm
then θ is
(A) 10π
13
(B) 9π
13
5π
(C) 13 (D) 6π
13

14. For the function f (x) = ecos x , Rolle’s theorem is

(A) applicable when 0 ≤ x ≤ π2 (B) applicable when π2 ≤ x ≤ 3π
2
(C) applicable when π4 ≤ x ≤ π2 (D) applicable when 0 ≤ x ≤ π

15. If p and q are coefficients of xn in the expansions of (1+x)2n and (1+x)2n−1
respectively, then pq is equal to

(A) 4 (B) 1
(C) 9 (D) 2

16. If α and β are the roots of the equation x2 + x + 1 = 0, then the equation
whose roots are α19 and β 7 is

(A) x2 − x + 1 = 0 (B) x2 + x − 1 = 0
(C) x2 + x + 1 = 0 (D) x2 − x − 1 = 0

17. The even function of the following is
x x
(A) f (x) = aax +a +1
(B) f (x) = aax −1
−x
−a−x
ax −1
√
(C) f (x) = x ax +1 (D) f (x) = log2 (x + x2 + 1)

3

18. There are 30 questions in multiple choice test. A student gets 1 mark for
each unanswered question, 0 marks for each wrong answer and 4 marks for
each correct answer. A student answered x questions correctly and scored 60
marks. Then the number of possible values of x is

(A) 15 (B) 10
(C) 6 (D) 5

2z + 1
19. If the imaginary part of is −2, then locus of the point representing z
iz + 1
in the complex plane is

(A) a circle (B) a straight line
(C) a parabola (D) an ellipse

20. If ω is a cube root of unity, then (3 + 5ω + 3ω 2 )2 + (3 + 3ω + 5ω 2 )2 is equal to

(A) 4 (B) 0
(C) -4 (D) -1

21. The harmonic mean of the roots of the equation
√ √ √
(5 + 2)x2 − (4 + 3)x + 8 + 2 3 = 0 is

(A) 2 (B) 4
(C) 6 (D) 8

22. If x, y, z are in HP, then log(x + z)log(x − 2y + z) is equal to

(A) log(x − z) (B) 2log(x − z)
(C) 3log(x − z) (D) 4log(x − z)

4

23. The interior angles of a polygon are in AP. The smallest angle is 120◦ and
the common difference is 5◦ . The number of sides of the polygon is

(A) 9 (B) 10
(C) 16 (D) 5

24. For every real number x, let f (x) = 1!x + 2!3 x2 + 3!7 x3 + 15
4!
x4 + . . . . Then the
equation f (x) = 0 has

(A) no real solution (B) exactly one real solution
(C) exactly two real solutions (D) infinite number of real solutions

25. Let p, q be real numbers. If α is the root of x2 +3p2 x+5q 2 = 0, β is a root of
x2 + 9p2 x + 15q 2 = 0 and 0 < α < β, then the equation x2 + 6p2 x + 10q 2 = 0
has a root γ that always satisfies

(A) γ = α4 + β (B) β < γ
(C) α < γ < β (D) γ = α2 + β

26. Let I denote the 3 × 3 identity matrix and P be a matrix obtained by
rearranging the columns of I. Then

(A) There are six distinct choices for P and det(P ) = 1
(B) There are six distinct choices for P and det(P ) = ±1
(C) There are more than one choices for P and some of them are not invert-
ible
(D) There are more than one choices for P and P −1 = I in each choice

27. If ax = by = cz = dw , the value of x( y1 + z1 + w1 ) is

(A) loga (abc) (B) loga (bcd)
(C) logb (cda) (D) logc (dab)

5

28. The sum of the first n terms of the series 12 + 2.22 + 32 + 2.42 + 52 + 2.62 + . . .
2
is n(n+1)
2
when n is even. For an odd n, the sum is

3n(n + 1) n2 (n + 1)
(A) (B)
2 2
n(n + 1)2 n2 (n + 1)2
(C) (D)
4 2

29. Let f (x) be a quadratic polynomial with f (2) = 10 and f (−2) = −2 . Then
the coefficient of x in f (x) is

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

30. The three sides of a triangle are distinct positive integers in an A.P. If the
smallest side is 10, the number of such triangles is

(A) 8 (B) 9
(C) 100 (D) infinite

31. The solution of the inequality 1 + |x − 1| ≥ 0 is

(A) (−∞, 0) (B) R
(C) (−2, 0) (D) (0, 2)

32. The function f (x) = x2 + bx + c, where b and c real constants, describes

(A) one-to-one mapping
(B) onto mapping
(C) not one-to-one but onto mapping
(D) neither one-to-one nor onto mapping

6

33. Let R be the set of all real numbers and f : [−1, 1] → R be defined by
x sin 1 x 6= 0
x
f (x) =
0 x=0
(A) f satisfies the conditions of Roll’s theorem on [1, 1]
(B) f satisfies the conditions of Lagrange’s Mean Value Theorem on [1, 1]
(C) f satisfies the conditions of Rolle’s theorem on [0, 1]
(D) f satisfies the conditions of Lagrange’s Mean Value Theorem on [0, 1]

34. A regular octagon was formed by cutting congruent isosceles right angled tri-
angles from the corner of a unit square. The side length of the octagon is

√
2−1 √
(A) (B) 2−1
√ 2 √
5−1 5−1
(C) (D)
4 2

35. The number of solutions of sin x = x6 in 0 ≤ x ≤ 12π is

(A) 1 (B) 6
(C) 10 (D) 12

√
36. If f (x) = x4 + 9x3 + 35x2 − x + 4 , then f (−5 + −4) is equal to

(A) -160 (B) 160
(C) 0 (D) 1

√ 2 √ 2
37. The solution of the equation (3 + 2 2)x −8 + (3 + 2 2)8−x = 6 are
√
(A) 3 ± 2 2 (B) ±1
√ √ √
(C) ±3 3, ±2 2 (D) ±3, ± 7

7

!3
1 1
38. The number of real roots of the equation x+ +x+ = 0 is
x x

(A) 0 (B) 2
(C) 4 (D) 6

39. The order of the differential equation of all parabolas whose axis of symmetry
along x -axis is

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

40. If ax2 +bx+c = 0 and 2x2 +3x+4 = 0 have a common root where a, b, c ∈ N
(set of natural numbers), the least value of a + b + c is

(A) 13 (B) 11
(C) 7 (D) 9

41. If m = n C2 , then m C2 is equal to
(A) 3 n C4 (B) n+1 C4
(C) 3 n+1 C4 (D) 3 n+1 C3

42. How many odd numbers of six significant digits can be formed with the digits
0,1,2,5,6,7 when no digit is repeated?

(A) 120 (B) 96
(C) 360 (D) 288

43. The coefficient of xn , where n is any positive integer, in the expansion of
1
(1 + 2x + 3x2 + . . . ∞) 2 is

n+1
(A) 1 (B)
2
(C) 2n + 1 (D) n + 1
8

44. If x, y and z are greater than 1, then the value of

1 logx y logx z

logy x 1 logy z is

logz x logz y 1

(A) log x log y log z (B) log x + log y + log z
(C) 0 (D) 1 − (log x log y log z)

45. Consider an ellipse with focii at (5, 15) and (21, 15). If the x-axis touches the
ellipse, then the length of the major axis is

(A) 17 (B) 34
√
(C) 13 (D) 416


 sin x2 , when x < 0;
x
46. Consider the function defined by f (x) =
x2 + ax + b whenx ≥ 0.
Suppose f (x) is differentiable on R, then

(A) a = 0, b = 0 (B) a = 1, b = 0
(C) a = 0, b = 1 (D) a = 1, b = 1


 x3 x≥1
47. If f (x) =
ax2 + bx + c x<1
where a, b and c are constants such that has second derivative at x = 1 . Then
a equals

(A) -6 (B) -3
(C) 6 (D) 3

9

48. A coin is tossed five times. If the outcomes are 2 heads and 3 tails (in same
order), then what is the possibility that the fourth toss is a head?
(A) 41 (B) 52
(C) 12 (D) 35

49. If the function f : R → R is defined by f (x) = (x2 + 1)35 ∀x ∈ R, then f is

(A) one-one but not onto (B) onto but not one-one
(C) neither one-one nor onto (D) both one-one and onto

50. If C is the reflection of A(2, 4) in x -axis and B is the reflection of C in
y -axis, then |AB| is
√
(A) 20 (B) 2 5
√
(C) 4 5 (D) 4

51. Let ω be the complex number cos 2π
3
+ i sin 2π
3
. Then the number of distinct

z+1 ω ω2

complex numbers z satisfying ω z + ω2 1 = 0 is equal to

ω2 1 z+ω

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

52. If A and B are square matrices of the same order such that (A+B)(A−B) =
A2 − B 2 , then (ABA−1 )2 is equal to

(A) B 2 (B) I
(C) A2 B 2 (D) A2

10

53. ABCD is a square with A = (1, 2) and B = (3, −4). If line CD passes
through (3, 8), then the mid point of CD is

(A) (2, 6) (B) (6, 2)
(C) (2, 5) (D) ( 28 , 1)
5 5

54. Using binomial theorem, the value of (0.999)3 correct to 3 decimal places is

(A) 0.998 (B) 0.999
(C) 0.996 (D) 0.997

2
55. The simplified form of q √ √ is
2+ 2+ 2+2 cos 4x

(A) sec x2 (B) sec x
(C) cos x (D) 1

56. The lines x + 2y + 3 = 0, x + 2y − 7 = 0 and 2x − y − 4 = 0 are three sides
of a square. Equation of the remaining side of the square can be

(A) 2x − y − 14 = 0 (B) 2x − y + 8 = 0
(C) 2x − y − 10 = 0 (D) 2x − y − 6 = 0

√
57. The equation 3 sin x + cos x = 4 has

(A) only one solution (B) two solutions
(C) infinitely many solutions (D) no solution

58. If the angle between tangents drawn to x2 + y 2 + 2gx + 2f y + c = 0 from
(0, 0) is π2 , then

(A) g 2 + f 2 = 3c (B) g 2 + f 2 = 2c
(C) g 2 + f 2 = 5c (D) g 2 + f 2 = 4c

11

59. Let P be the point (1, 0) and Q a point on the locus y 2 = 8x. The locus of
the mid point of P Q is

(A) x2 − 4y + 2 = 0 (B) x2 + 4y + 2 = 0
(C) y 2 + 4x + 2 = 0 (D) y 2 − 4x + 2 = 0

60. The number of values of c such that the line y = 4x + c touches the curve
x2
4
+ y 4 = 1, is

(A) 1 (B) 2
(C) ∞ (D) 0

61. If the sum of distances from a point P on two mutually perpendicular straight
lines is 1 unit, then the locus of P is

(A) a parabola (B) a circle
(C) an ellipse (D) a straight line

√
62. The function f (x) = sec(log(x + 1 + x2 )) is

(A) odd (B) even
(C) neither odd nor even (D) constant

d y2
π 3 3
63. The second order derivative dx 2 at t = 4 where x = a sin t and y = a cos t

is
1
(A) 2 (B) 12a
√
(C) 43a2 (D) 43a
√
2

64. If y = cos−1 (cosx), then y ′ (x) =

(A) 1 for all x (B) -1 for all x
(C) 1 in second and third quadrant (D) -1 in third and fourth quadrant

12

dy
65. If x2 + y 2 = t − 1t and x4 + y 4 = t2 + t12 , then dx =

(A) x21y3 (B) xy1 3
(C) x21y2 (D) x13 y

66. If y = lim (1 + x)(1 + x2 )(1 + x4 ) . . . (1 + x2n ), and x2 < 1, then y ′ is equal
n→∞
to
1
(A) 1 (B) 1−x
1 −1
(C) (1−x) 2 (D) (1−x) 2

67. The points (k − 1, k + 2), (k, k + 1), (k + 1, k) are collinear for

(A) any value of k (B) k = −1/2 only
(C) no value of k (D) integral values of k only

68. One ticket is selected at random from 50 tickets numbered 00, 01, 02, . . . 49.
Then the probability that the sum of the digits on the selected ticket is 8,
given that the product of these digits is zero, equals
5 1
(A) 14 (B) 50
(C) 17 1
(D) 14

69. A focus of an ellipse is at the origin. The directrix is the line x = 4 and the
eccentricity is 12 . Then the length of the semi-major axis is

(A) 38 (B) 32
(C) 43 (D) 53

dy
70. If y = |cosx| + |sinx|, then dx at x = 2π
3
is

(A) 0 (B) 1
√ √
(C) 1−2 3 (D) 3−12

13

71. Let f : R → R be a positive increasing function with limx→∞ ff(3x)
(x)
= 1. Then
limx→∞ ff(2x)
(x)
=

(A) 23 (B) 3
(C) 1 (D) 32

72. Let R be the real line. Consider the following subsets of the plane R × R :
S = {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y) : x − 1 is an integer}.
Which one of the following is true?

(A) Neither S nor T is an equivalence relation on R
(B) Both S and T are equivalence relations on R
(C) S is an equivalence relation on R but T is not
(D) T is an equivalence relation on R but S is not

dy
73. If sin y = x sin(a + y), then dx is
2
(A) sinsin a
2 (a+y) (B) sinsin
(a+y)
a
2
(C) sin a sin2 (a + y) (D) sinsin
(a−y)
a

74. The non-zero vectors a, b and c are related by a = 8b and c = −7b. Then
the angle between a and c is

(A) 0 (B) π2
(C) π (D) π4

75. The domain of the function f (x) = cot−1 ( √ 2x ), for real x ∈ R (here [x]
x −[x2 ]
is the largest integer less than x ) is
√ √
(A) R − {± n, n ∈ N} (B) R − { n : n ≥ 0, n ∈ I}
(C) R (D) R − {0}

14

76. Number of real solutions of the equation x7 + 14x5 + 16x3 + 30x − 560 = 0 is

(A) 7 (B) 1
(C) 3 (D) 5

77. The value of n ∈ I for which the function f (x) = sin nx
sin nx has 4π as its period,
is

(A) 2 (B)3
(C) 4 (D) 5

78. The differential equation of the family of circles with fixed radius 5 units and
center on the line y = 2 is

(A) (y − 2)2 y ′2 = 25 − (y − 2)2 (B) (x − 2)2 y ′2 = 25 − (y − 2)2
(C) (y − 2)y ′2 = 25 − (y − 2)2 (D) (x − 2)y ′2 = 25 − (y − 2)2

2
79. The domain of the function sin−1 (log2 x2 ) is

(A) [−1, 2]−{0} (B) [−2, 2]−(−1, 1)
(C) [−2, 2] − {0} (D) [1, 2]

80. The quadratic equations x2 − 6x + a = 0 and x2 − cx + 6 = 0 have one root
in common. The other roots of the first and second equations are integers in
the ratio 4 : 3. Then the common root is

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

15

81. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary
are to be selected and arranged in a row on a shelf so that the dictionary is
always in the middle. Then the number of such arrangement is

(A) at least 750 but less than 1000 (B) at least 1000
(C) at least 500 but less than 750 (D) less than 500

82. If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C,
then

(A) A = C (B) B = C
(C) A ∩ B = φ (D) A = B

83. If the roots of the equation bx2 + cx + a = 0 be imaginary, then for all real
values of x, the expression 3b2 x2 + 6bcx + 2c2 is

(A) less than −4ab (B) greater than −4ab
(C) less than 4ab (D) greater than 4ab

s
x
84. The domain of the real function f (x) = x− is
1−x
(A) [1, ∞) (B) (−∞, 1)
(C) (−∞, 1] (D) (1, ∞) ∪ {0}

85. If f (x).f ( x1 ) = f (x) + f ( x1 ) and f (4) = 65, then f (6)

(A) 65 (B) 217
(C) 215 (D) 64

√
4 2 − (cos x + sin x)5
86. limπ =
x→ 4 1 − sin 2x
√ √
(A) 5 2 (B) 3 2
√ √
(C) 2 (D) 7 2
16

87. The number of sides of a polygon with 44 diagonals is

(A) 10 (B) 11
(C) 12 (D) 13

2
88. If f (2) = 2 and f ′ (2) = 1, then lim 2x x−2
−4f (x)
=
x→2

(A) 4 (B) -4
(C) 2 (D) -2



 x−1 x < 0;



89. For the function f (x) = 1 x = 0;

 4


 x2 x > 0.

lim f (x) and lim− f (x) are
x→0+ x→0

(A) 0, 1 (B) 0, -1
(C) 1, -1 (D) -2,-1

√ √
90. The value of x for which 1 + x log (x + x2 + 1) ≥ 1 + x2 are

(A) x ≤ 0 (B) 0 ≤ x ≤ 1
(C) x ≥ 0 (D) x ≤ 1

91. The maximum value of sin x + 21 sin 2x + 13 sin 3x, 0 ≤ x ≤ π2 , is
√ √
(A) 1 + 2 2 (B) 2 2 − 1
√
(C) 1 − 2 2 (D) 12 + 3√4 2

17




x + 2
 −1 ≤ x ≤ 0;
92. Let f (x) = 1 x = 0;



x
2
0 < x ≤ 1.
Then on [−1, 1] this function has

(A) a minimum (B) a maximum
(C) neither a minimum nor a minimum (D) f ′ (x) dose not exist

R 1
93. 1+cos x+sin x
dx =

(A) log |1 + tan x2 | + c (B) 21 log |1 + tan x2 | + c
(C) 2 log |1 + tan x2 | + c (D) 21 log |1 − tan x2 | + c

R sin x cos x
94. √ dx =
1−sin4 x

(A) 12 sin−1 (sin2 x) + c (B) 21 cos−1 (sin2 x) + c
(C) tan−1 (sin2 x) + c (D) tan−1 (2 sin2 x) + c

R dx
95. x(xn +1)
is equal to
n
n

(A) n1 log xnx+1 +c (B) n1 log x x+1
n +c
n
1 xn


(C) log xnx+1 + c (D) n log xn −1 + c

R π2
96. − π2 sin |x|dx is equal to

(A) 0 (B) 1
(C) 2 (D) π

R 4 √x
97. The value of 1
e dx is

(A) e2 (B) 2e2
(C) 4e2 (D) 3e2

18

√ √
98. The area bounded by the curves x+ y = 1 and x + y = 1 , is

(A) 31 sq unit (B) 16 sq unit
(C) 21 sq unit (D) 51 sq unit

dy


99. A particular solution of log dx
= 3x + 4y , y(0) = 0 is

(A) e3x + 3e−2y = 4 (B) 4e3x − 3x−4y = 3
(C) 3e3x + 4e−4y = 7 (D) 4e3x + 3e−4y = 7

100. The vectors ~a = bi + b k , ~b = bi + b
j + mb j + (m + 1)b j + mb
k and ~c = bi − b k are
coplanar

(A) if m = 1 (B) if m = 4
(C) if m = 3 (D) for no value of m

(~a × ~b)2 + (~a.~b)2
101. The value of is
2~a2 .~b2
(A) ~a.~b (B) 1
(C) 0 (D) 12

22 + 42 + · · · (2n)2
102. For, to exceed 1.01 , the maximum value of n is
11 + 22 + · · · + (2n − 1)2
(A) 99 (B) 100
(C) 101 (D) 150

103. Tangents to a circle at points P and Q on the circle meet at a point R. If
P Q = 6 and P R = 5, then radius of the circle is

(A) 13
3
(B) 4
(C) 15
4
(D) 15
5

19

104. Number of distinct primes dividing 12 ! + 13 ! + 14 ! is

(A) 5 (B) 6
(C) 7 (D) 8

105. If the quadratic polynomial f (x) = ax2 + bx + c has positive coefficients a, b, c
in AP in that order. If f (x) = 0 has integer roots α, β , then α + β + αβ is

(A) 3 (B) 5
(C) 7 (D)14

x+c
106. If y = where c is a constant and y is stationary, then xy is equal to
1 + x2
(A) 21 (B) 43
(C) 13 (D) 14

107. The probability that event A occur is 43 and the probability the B occur is
2
3
. Minimum and maximum possible values of P (A ∩ B) is
5 2 5 3
(A) 12 ,3 (B) 12 ,4
2 3 5 1
(C) 3 , 4 (D) 12 , 2

108. A straight line through (-3,4) be such that the portion intercepted by the axes
is divided at (-3,4) in the ratio 4:1 externally, then which of the following is
not a point on the line

(A) (9,0) (B) ( − 12 , 19
6
)
(C) (3,1) (D) ( -3,4)

109. The system of equations x + 32 y + 31 z = 0 , y + 2z = 0, x + 34 + 53 z = 0 posses

(A) no solution (B) only trivial solution
(C) infinite non-trial solutions (D) one non-trivial solution

20

110. A bird is sitting on the top at a vertical pole of height 20 m and elevation
from a point 0 on the ground is 45o . The bird from the top of the pole flies off
horizontally away from the pole. After one second, the elevation of the bird
from 0 is reduced to 30o , then the speed of the bird is
√ √ √
(A) 40( 3 − 2) (B) 20 2
√ √
(C) 20( 3 − 1) (D) 40( 2 − 1)

111. All the thirteen spade cards are drawn from a pack and formed a new pack.
From these 13 spade cards, cards are drawn one by one without replacement
till the ace of spade comes. The probability the ace comes in the fourth draw
is
1 12
(A) 13 (B) 13
9 4
(C) 13 (D) 13

112. The point of intersection of the tangents drawn to the curve x2 y = 1 − y at
the point where it is met by the curve xy = 1 − y is given by

(A) (0,-1) (B) (1,1)
(C) (0,1) (D) (-1, -1)

113. Three positive numbers form an increasing G.P. If the middle term in the G.P.
is doubled the three numbers are in an A.P. Then the common ratio of the
G.P. is
√ √
(A) 3 + 2 (B) 2 − 3
√ √ √
(C) 2 + 3 (D) 2 − 3

114. A problem in mathematics is given to three students A, B, C and their respec-
tive probability of solving the problem is 12 , 13 , 41 . Probability that the problem
is solved is

(A) 34 (B) 21
(C) 23 (D) 13
21

115. The equations of tangent and normal to the curve y = x4 −6x3 +13x2 −10x+5
at the point (1,3) are

(A) 2x − y + 1 = 0, 2x + y + 1 = 0 (B) x + 2y − 7 = 0, x + 2y + 7 = 0
(C) 2x − y + 1 = 0, x + 2y − 7 = 0 (D) 2x + y + 1 = 0, x + 2y + 7 = 0

x+2 y+1 z−3
116. Coordinates of the points on the line + + at a distance 5
3 2 2
units from the point (1,3,3) are

(A) (3,7,4), (-2,-1,3) (B) (7,4,3), (2,-1,3)
(C) (4,3,7),(-2,-1,3) (D) (1,0,1),(-2,1,3)

117. Geetha and Somu appear for an interview for two vacancies in a company. The
probability of Geethas selection is 15 and Somu is 61 . Then the probability that
(i) both of them are selected (ii) both of them are not selected are respectively
1 2 1 2
(A) 30 ,5 (B) 30 ,3
7 2 7 2
(C) 30 , 3 (D) 30 , 3

118. The set of homogenous equations tx + (t + 1)y + (t − 1)z = 0, (t + 1)x + ty +
(t + 2)z = 0, (t − 1)x + (t + 2)y + tz = 0 has non-trivial solutions for

(A) three values of t (B) two values of t
(C) one value of t (D) no value of t

119. The points (0, 38 ), (1, 3), (82, 30)

(A) from an obtuse angled triangle (B) from an acute angled triangle
(C) from a right angled triangle (D) lie on a straight line

22

120. A straight line is normal to both the parabolas y 2 = x and x2 = y . The
distance of the origin from it is

(A) 4√3 2 (B) 2√1 2
(C) √12 (D) 3√1 2

Rπ sin2 x
121. e cos2 xdx =
0

(A) 0 (B) −1
(C) 1 (D) π

dy
122. The solution of the differential equation e dx = x + 1 when y(0) = 3

(A) y = x log x − x + 2 (B) y = (x + 1) log(|x + 1|) − x + 3
(C) y = (x + 1) log(|x + 1|) + x + 3 (D) y = x log x + x + 3

x−2 y−1 z+2
123. Let the line = = lie in the plane x + 3y − αz + β = 0, then
3 −5 2
(α, β) lie on
(A) x + y = 1 (B) x − y = 1
(C) x + y = 13 (D) x − y = 2

1 x x2

124. The equation x2 1x = 0 has

x x2 1

(A) exactly two distinct roots (B) one pair of real equal roots
(C) three pairs of equal roots (D) modulus of each root is 2

23

125. n-similar balls each of weight x when weighed in pairs the sum of the weights
of all possible pairs is 120 when they are weighed in triplets the sum of the
weights comes out to be 480 for all possible triplets, then x is

(A) 5 (B) 10
(C) 15 (D) 20

24

PHYSICS

126. A heater coil is cut into two equal parts and only one part is used for heating. The
heat generated will now be

(A) doubled (B) four times
(C) one fourth (D) halved

127. The material suitable for making electromagnets should have

(A) high retentivity and high coercivity
(B) low retentivity and low coercivity
(C) high retentivity and low coercivity
(D) low retentivity and high coercivity

128. A particle moves in a straight line with retardation proportional to its displacement.
Its loss of kinetic energy for any displacement x is proportional to

(A) x2 (B) ex
(C) x (D) loge x

129. The electric charge of the neutrino is given by

(A) 1 (B) ‒1
(C) 0 (D) 2

130. The sun releases energy by

(A) nuclear fission (B) nuclear fusion
(C) spontaneous combustion (D) hydro-thermal process

131. A semiconductor with equal concentration of acceptor and donor type impurities is
termed as

(A) compensated (B) intrinsic
(C) amphoteric (D) None of the above

132. X-rays consists of

(A) negatively charged particles (B) electromagnetic radiation
(C) a stream of neutrons (D) positively charged particles

133. Copper crystallizes in fcc lattice with a unit cell edge of 361 pm. The radius of
copper atom is

(A) 108 pm (B) 128 pm
(C) 157 pm (D) 181 pm

2

134. A container with insulating walls is divided into equal parts by a partition fitted with a
valve. One part is filled with an ideal gas at a pressure P and temperature T, whereas
the other part is completely evacuated. If the valve is suddenly opened, the pressure
and temperature of the gas will be

(A) P/2, T/2 (B) P, T
(C) P, T/2 (D) P/2, T

135. The commutator bracket  XY , Z  is expanded as

(A)  X , Z    X ,Y  (B)  X , Z Y  Z Y , Z 
(C) Z  X , Z   Y , X  Z (D) Z,Y    X , Z 
136. The force carrier in the case of EM waves is

(A) a photon (B) a proton
(C) a pion (D) an electron

137. Any f-orbit can accommodate upto

(A) fourteen electrons (B) nine electrons
(C) ten electrons (D) eighteen electrons

138. The unit of magnetic flux would be

(A) Wb (B) Wb  m 2
(C) Ampere-Coulomb (D) Wb / m 2

139. A calcite crystal is placed over a dot on a piece of paper and rotated. On seeing
through the calcite, one will see

(A) two rotating dots
(B) two stationary dots
(C) one dot only
(D) one dot rotating about the other

140. Assume that a neutron breaks into a proton and an electron. The energy released
during this process is
(mass of neutron = 1.6725×10‒27 kg, mass of proton = 1.6725×10‒27 kg, mass of
electron 9.6725×10‒31 kg)

(A) 0.73 MeV (B) 7.10 MeV
(C) 6.30 MeV (D) 5.4 MeV

141. The angle between electric and magnetic field in an electromagnetic wave travelling
in vacuum is

(A) 2 (B) 2 / 3

3

(C)  /2 (D) 4

142. According to Bohr’s principle the relation between main quantum number n and
radius r of the orbit is

1 1
(A) r (B) r
n n2
(C) r n (D) r  n2

143. Two wires are made of the same material and have the same volume. However, wire
1 has cross-sectional area A and wire 2 has cross-sectional area 3A. If the length of
wire 1 increases by x on applying force F, the force needed to stretch wire 2 by the
same amount is

(A) F (B) 4F
(C) 6F (D) 9F

144. The surface of metal is illuminated with the light of 400 nm. The kinetic energy of
the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is
(hc = 1240 eV.nm)

(A) 3.09 eV (B) 1.41 eV
(C) 1.51 eV (D) 1.68 eV

145. Which of the following Poisson brackets is non-vanishing?

(A) q , p 
i j (B) p,p  i j

(C)  q , p  if i  j
i j (D)  q , p  if i  j
i j

146. A particle is acted on by forces given in newtons by F1  10iˆ  4 ˆj and F2  17iˆ  2 ˆj .
The force F3 which balances these forces is

(A) F1  10iˆ  4 ˆjN (B) F1  27iˆ  2 ˆjN
(C) F1  27iˆ  4 ˆjN (D) F1  12iˆ  6 ˆjN

147. If pressure is increased on a piece of wax, the melting point of wax

(A) decreases (B) does not change
(C) increases (D) decreases at first then increases

148. Which one of the following particle is a boson?

(A) Photon (B) Proton
(C) Neutron (D) Electron

4

149. What is the dimensional formula of specific heat?

(A) [M L‒2 T‒2] (B) [M0 L2 T‒2 K‒1]
(C) [M0 L T‒2] (D) [M L T‒2]

150. Which of the following pairs of physical quantities have different dimensions?

(A) Stress, pressure (B) Young’s modulus, energy
(C) Density, relative density (D) Energy, torque

151. A bus starts from rest with an acceleration of 1 m/sec2. A man who is 48 m
behind the bus starts with a uniform velocity of 10 ms-1. Then after how much
time the man will catch the bus?

(A) 12 sec (B) 8 sec
(C) 10 sec (D) 4 sec

152. Which of the following force is conservative?

(A) Gravitational force (B) Frictional force
(C) Air resistance (D) Viscous force

153. A particle moves in a plane with uniform acceleration having direction
different than that of instantaneous velocity. What is the nature of trajectory?

(A) Straight line (B) Parabola
(C) Circle (D) Ellipse
  
154. In a uniform circular motion r , V and  stands for radius vector, linear
velocity and angular velocity respectively. Then which of the following is
true?

     
(A) V  r   (B) V    r
  
(C) V  r .  (D) None of the above

155. Angular momentum is

(A) an axial vector (B) a polar vector
(C) a scalar (D) None of the above

5

156. Which of the following surfaces in contact has maximum coefficient
of friction    ?

(A) Wood on wood (B) Rubber tyre and dry concrete
(C) Steel on steel (D) Rubber tyre on wet concrete

157. The tidal waves in the sea are primarily due to

(A) atmosphere of the Earth
(B) gravitational effect of Venus on the Earth
(C) gravitational effect of Sun on the Earth
(D) gravitational effect of Moon on the Earth

158. The total energy of the particle executing Simple Harmonic Motion is

(A) proportional to x (B) proportional to
(C) independent of x (D) proportional to

159. When the intermolecular distance decreases due to compressive force, there is

(A) zero resultant force between molecules
(B) repulsive force between molecules
(C) attractive force between molecules
(D) no force between molecules

160. If S is stress and Y is Young’s modulus of material of a wire, the energy stored
in the wire per unit volume is

(A) 2 S2 Y (B) S2 / 2Y
(C) 2 Y / S2 (D) S / Y

161. The pressure at the bottom of a tank of liquid is not proportional to

(A) the density of the liquid (B) area of the liquid surface
(C) the height of the liquid (D) the acceleration

162. Persons sitting in an artificial satellite circling around the earth have

(A) zero mass (B) zero weight
(C) infinite weight (D) infinite mass

6

163. A satellite is orbiting round the earth in a circular orbit with speed v. If m is
mass of satellite, its total energy is

1
(A) mv 2 (B) mv 2
2
1 3
(C)  mv 2 (D) mv 2
2 4

164. Which one of the following is most elastic in nature?

(A) Rubber (B) Steel
(C) Copper (D) Putty

165. A bucketful of water is kept in a room and it cools from 75°C to 70°C in
T1 min, from 70°C to 65°C in T2 min, and from 65°C to 60°C in T3 min. Then

(A) T1= T2 (B) T1< T2< T3
(C) T1> T2> T3 (D) T1< T3 < T2

166. If a star emitting orange light moves away from the Earth, its colour will

(A) appear red (B) appear yellow
(C) remain the same (D) turns gradually blue

167. The wavelength of light coming from a star shifts towards the violet end of the
spectrum. This shows that star is

(A) receding from the earth
(B) approaching the earth
(C) neither approaching nor receding from the earth
(D) sometimes approaching and sometimes receding from the earth

168. When sound travels from air to water the quantity that remains unchanged is

(A) speed (B) frequency
(C) intensity (D) wavelength

169. The thermodynamic process in which the pressure of system remains constant
is called

(A) Isochoric (B) Adiabatic
(C) Isothermal (D) Isobaric

7

170. The source and sink temperature of a Carnot engine are 400K and 300K
respectively. What is the efficiency?

(A) 100% (B) 75%
(C) 33.3% (D) 25%

171. If the temperature of the source and sink is increased by the same amount, the
efficiency of the engine

(A) decreases (B) increases
(C) remains unchanged (D) may increase or decrease

172. The diamagnetic material has susceptibility

(A) χ = 0 (B) χ < 1
(C) χ > 1 (D) χ < 0

173. Curie temperature is the temperature above which

(A) a paramagnetic material becomes diamagnetic
(B) a ferromagnetic material becomes diamagnetic
(C) a paramagnetic material becomes ferromagnetic
(D) a ferromagnetic material becomes paramagnetic

174. The wavelength of thermal radiation is

(A) less than that of the visible light
(B) greater than that of the visible light
(C) equal to that of the visible light
(D) far shorter than that of the visible light

175. If  0 and 0 are the electric permittivity and magnetic permeability in free
space,  and  are the corresponding quantities in a medium, then index of
refraction of the medium is

 0 
(A) (B)
0 0
 0 0 
(C) (D)
  0 0

176. An electron with kinetic energy 5 eV is incident on a hydrogen atom in its
ground state. The collision

(A) may be completely inelastic (B) must be completely inelastic
(C) may be partially inelastic (D) must be elastic

8

177. The phenomenon of emission of electron from hot bodies is called

(A) thermionic emission (B) photoelectric emission
(C) field emission (D) secondary emission

178. The diode is used as

(A) an amplifier (B) an oscillator
(C) a rectifier (D) a modulator

179. A water tap leaks such that water drops fall at regular intervals. Tap is fixed 5 m
above the ground. First drop reaches the ground when 4th drop is about to leave the
tap. Find the separation between 2nd and 3rd drop.

(A) 2/3 m (B) 4/3 m
(C) 5/3 m (D) None of the above

180. A cube of side ‘a’ is placed on an inclined plane of inclination . What is the
maximum value of θ for which cube will not topple?

(A) 15° (B) 30°
(C) 45° (D) 60°

181. Two spherical soap bubbles of radii R1 and R2 combine under isothermal condition to
form a single bubble. The radius of the resultant bubble is

(A) R = + (B) R =

(C) R = (D) R=

182. Variation of molar specific heat of a metal with temperature is best depicted by
The image part w ith relationship I D rId115 w as not found in the file. The image part w ith relationship I D rId116 w as not found in the file.

(A) (B)

The image part w ith relationship I D rId118 w as not found in the file.
The image part w ith relationship I D rId117 w as not found in the file.

(C) (D)

9

183. A thin metal sheet is introduced in between a parallel plate capacitor having
capacitance C. Then

(A) capacitance remains still (B) capacitance > C
(C) capacitance < C (D) capacitance becomes ∞

184. Two wires of same material having length l and 2l and cross sectional areas 4A and A
respectively. The ratio of their specific resistances would be

(A) 1 : 2 (B) 8 : 1
(C) 1 : 8 (D) 1 : 1

185. A charged particle moves through a magnetic field in a direction perpendicular to it.
Then the

(A) velocity remains unchanged (B) speed remains unchanged
(C) direction remains unchanged (D) acceleration remains unchanged

186. The magnetic field at the centre of circular coil of radius r carrying current I is B1.
The field at the centre of another coil of radius 2r carrying same current I is B2. The
ratio of B1/B2 is

(A) 1 (B) ½
(C) 2 (D) 4

187. The mass of photon at rest is

(A) Zero (B) hγ
(C) hc/λ (D) hγ/c

188. To use a transistor as an amplifier

(A) the emitter base junction is forward biased and the base collector junction is
reverse biased
(B) no voltage required
(C) both junctions are forward biased
(D) both junctions are reverse biased

189. In Rutherford scattering experiment, what will be the correct angle of scattering for an
impact parameter b = 0?

(A) 90° (B) 270°
(C) 0° (D) 180°

10

190. In an npn transistor circuit, the collector current is 10mA. If 90% of the electrons
emitted reach the collector, then

(A) the emitter current will be 9 mA
(B) the emitter current will be 10mA
(C) the base current will be 1 mA
(D) the base current will be ‒1 mA

191. When distance between two point charges (one positive and the other negative) is
halved, then the electrostatic force between the charges will

(A) increase two times (B) decrease two times
(C) increase four times (D) decrease four times

192. Two resistors of equal value are connected in series and the total resistance is Rseries.
When the same two resistors are connected in parallel then the total resistance is
Rparallel. The ratio between Rseries to Rparallel is

(A) 2 (B) 3
(C) 4 (D) 6

193. When a simple pendulum bob is made to oscillate in water, then the time period will

(A) increase (B) decrease
(C) remain unchanged (D) immediately come to rest

194. X-rays are used as a tool to study the properties of single crystals, since

(A) X-ray energies are comparable with the crystal cohesive energy
(B) X-ray wavelengths are comparable with the crystal spacing
(C) X-rays are easily absorbed by the crystal
(D) X-rays are transparent to crystal

195. Oil is used for frying food materials rather than water, since oil

(A) viscosity is high (B) vapour pressure is high
(C) density is high (D) boiling point is high

196. Mirage is the illusion of presence of water on the surface of earth. This is due to the

(A) dispersion (B) Rayleigh scattering
(C) total external reflection (D) total internal reflection

197. The volume of a nucleus in an atom is proportional to its

(A) mass number (B) proton number
(C) neutron number (D) electron number

11

198. Pitch of the sound depends on

(A) loudness (B) quality
(C) frequency (D) amplitude

199. Water is a

(A) liner molecule (B) planar molecule
(C) tetrahedral molecule (D) octahedral molecule

200. If the valence electrons exactly fill one or more bands, leaving others empty, then the
crystal will be

(A) insulator (B) conductor
(C) semiconductor (D) metal

CHEMISTRY

201. An alkene having the molecular formula C9H18 on ozonolysis gives
2,2-dimethylpropanal and 2-butanone. The alkene is

(A) 2,2,4-trimethyl-3-hexene (B) 2,2,6-trimethyl-3-hexene
(C) 2,3,4-trimethyl-2-hexene (D) 2,2,4-trimethyl-2-hexene

202. The compound C4H10O can show

(A) metamerism (B) function isomerism
(C) position isomerism (D) all types

203. Which of the following is not aromatic?

(A) Cyclopentadienyl cation (B) Cyclopentadienyl anion
(C) Cycloheptatrienyl cation (D) Anthracene

204. Consider the following carbocations
(a) Cl3C+ (b) Cl2CH+ (c) ClCH2+ (d) CH3+

The stability sequence follows the order

(A) (d) < (a) < (b) < (c) (B) (a) < (b) < (c) < (d)
(C) (d) < (a) < (c) < (b) (D) (d) < (b) < (a) < (c)

205.

(A) pyruvic acid (B) propanoic acid
(C) α-hydroxy propanal (D) malonic acid

206. Allyl chloride on treatment with triethylamine, it gives

12

(A) propadiene (B) propylene
(C) allyl alcohol (D) actone

207. Aldehydes or ketones react with α-bromo esters and metallic zinc to yield

(A) δ-keto esters (B) β-keto alcohols
(C) β-hydroxyl esters (D) δ-hydroxyl esters

208. Reduction of cinnamic acid (Ph.CH=CH.COOH) with LiAlH4 gives the following
product

(A) Ph.CH2CH2COOH (B) Ph.CH=CH.CH2OH
(C) Ph.CH2CH2CH2OH (D) None of the above

209. An example of alkane with least number of carbon atoms which is optically
active is

(A) 2-methylpentane (B) 3-methylpentane
(C) 2-methylhexane (D) 3-methylhexane

210. Which of the following does not react with Fehlings solution?

(A) CH3-CH2-OH (B) CH3-O-CH3
(C) C6H5-CHO (D) All of the above

211. In the sequence of the reaction, the final product is

(A) ClCH2-COONH4 (B) ClCH2-CONH2
(C) Cl2CH-CONH2 (D) NH2-CH2-CONH2

212. Which one of the following amines reacts with chloroform and alkali to give
an isocyanide?

(A) (CH3)2NH (B) (C6H5)2NH
(C) C6H5-NH2 (D) (C2H5)3N

213. The reaction of carboxylic esters with Grignard reagents is an excellent method for
preparing

(A) aldehydes (B) alkanes
(C) primary alcohols (D) tertiary alcohols

214. Which of the following on dehydration with P2O5 will give ethanenitrile?

(A) ehanol (B) ethanamide
(C) propanamide (D) ethanol

13

215. Aniline was acetylated, then the resulting product on nitration followed by hydrolysis
gives

(A) o-nitro-acetanilide
(B) m-nitroaniline
(C) acetanilide
(D) a mixture of o-nitroaniline and p-nitroaniline

216. DNA molecules contain nitrogenous bases linked to other constituents of the
molecule. Which of the following is not found in DNA?

(A) guanidine (B) thymine
(C) adenine (D) guanine

14

217. The hydrogen ion concentration of a solution with pH value 3.69 is given by

(A) 2.042 × 10‒4 M (B) 3.69 × 10‒2 M
(C) 4.31 × 10‒4 M (D) 0.369 M

218. Which of the following two gases can be cooled from room temperature by the Joule-
Thomson effect?

(A) Hydrogen and oxygen (B) Helium and nitrogen
(C) Helium and hydrogen (D) Nitrogen and oxygen

219. Calculate the concentration of H2SO4 when 10 mL of 0.2 M of H2SO4 is added to
90 mL of H2O.

(A) 0.02 N (B) 0.04 M
(C) 0.04 N (D) 0.002 M

220. The increase in internal energy of the system is 100 J when 300 J heat is supplied to
it. What is the amount of work done by the system?

(A) –200 J (B) +200 J
(C) –300 J (D) –400 J

221. The efficiency of a heat engine is given by

W T −T W T −T
(A) = (B) =
q T q T
W T −T W T −T
(C) = (D) =
q T q T

222. A metallic element has a cubic lattice. Each edge of the unit cell is 2 Ǻ. The density of
the metal is 2.5 g cm‒3. The unit cells in 200g of the metal are

(A) 1×1025 (B) 1×1024
(C) 1×1022 (D) 1×1020

223. The hydrogen electrode is dipped in a solution of pH = 3 at 25 C, the potential of the
.
cell would be (the value of = 0.059 V)

(A) +0.177 V (B) –0.177 V
(C) +0.087 V (D) +0.

224. To protect iron against corrosion the most durable metal plating on it is

(A) Tin plating (B) Copper plating
(C) Zinc plating (D) Nickel plating

15

225. The half-life of a first order reaction

(A) depends on the reactant concentration raised to the first power
(B) is inversely proportional to the square of the reactant concentration
(C) is inversely proportional to the reactant concentration
(D) is totally independent of the reactant concentration

226. The pH of the blood is maintained by buffer system given by

(A) NaCl and HCl (B) NH4Cl and NH4OH
(C) Sodium citrate and citric acid (D) HCO3‒ and H2CO3

227. Which of the following sets of conditions makes a process spontaneous at all
temperatures?

(A) ∆H = 0; ∆S > 0 (B) ∆H = 0; ∆S < 0
(C) ∆H > 0; ∆S > 0 (D) ∆H < 0; ∆S > 0

228. How many Bravais lattices are possible in a crystal?

(A) 23 (B) 7
(C) 230 (D) 14

229. The Clausius-Clayperon equation helps to calculate

(A) Latent heat of vaporization (B) Melting point of the solvent
(C) Heat of neutralization (D) Molecular weight of solute

230. The solubility ‘s’ of a sparingly soluble salt is related to its equivalent conductance at
infinite dilution by the relation (k in specific conductance)

k × 1000 c × 1000
(A) s = (B) s =
l∞ − l l∞ − l

k × 1000 c × 1000
(C) s = (D) s =
l∞ l∞

231. Electrical conductivity of an electrolyte depends upon

(A) the number of molecules in the electrolytes
(B) the number of ions present in the electrolytes
(C) the number of charges carried by the ions
(D) the number of ions present in the solution and the number of charges
carried by the ions

232. The energy of an electron in an orbital depends on

(A) n (B) n, l
(C) n, l, m (D) n, l, m, ms

16

5 3 21 2
233. In the atomic spectrum of H, lines were observed at R, R, R and R
36 16 100 9
(R=Rydberg constant). It belongs to ……………... series.

(A) Lyman (B) Balmer
(C) Paschen (D) Pfund

234. Out of the oxides given below which of them cannot be reduced by H2 ?
I - Al2O3 ; II - CuO ; III - ZnO

(A) Only I (B) I and II
(C) I, II, III (D) III and II

235. In diamond the bonds present are

(A) ionic and covalent (B) covalent dative
(C) covalent only (D) electrovalent dative

236. A mixture of 3g of sulphur and 12.7g of copper was placed in a quartz tube. The tube
was sealed under vacuum and then heated to the melting. The cooled tube contains

(A) copper(I) sulphide
(B) mixture of copper (I) sulphide and copper
(C) mixture of sulphur and copper
(D) mixture of copper(I) sulphide and sulphur

237. Which of the following oxide cannot be used as reducing agent?

(A) SO2 (B) NO2
(C) CO2 (D) ClO2

238. Which of the following metal is the most abundant in the Earth’s crust?

(A) Mg (B) Na
(C) Ca (D) K

239. Which of the following is used as antacid in medicine?

(A) Milk of magnesium (B) Milk of lime
(C) Lime water (D) Baryta

240. Which of the following has the lowest melting point?

(A) Lithium (B) Potassium
(C) Sodium (D) Cesium

17

241. Which nitrogen trihalide is least basic?

(A) NF3 (B) NBr3
(C) NCl3 (D) NI3

242. Deep sea divers use the following mixture for respiration

(A) Oxygen and nitrogen (B) Oxygen and argon
(C) Oxygen and hydrogen (D) Oxygen and helium

243. Symmetric intermolecular hydrogen bonding is shown by which of the following
compound?

(A) HF2 (B) (HF)n
(C) Ice (D) H3BO3

244. Which one of the following element do not occur in nature?

(A) Mo (B) Re
(C) Tc (D) Pr

245. Hybridization of iron in K3[Fe(CN)6]

(A) sp3 (B) dsp3
(C) sp3d2 (D) d2sp3

246. Predict the element resulting from two  decay, two consecutive  decay and one 
decay of Th-232

(A) Ra (B) Po
(C) Th (D) Rn

247. The blue colour produced when a starch solution is added to a solution containing
traces of I2 and KI is due to
I) formation of I3－ II) formation of an inclusion complex
III) Oxidation of starch IV) Oxidation of I2

(A) I and II (B) I and III
(C) II and III (D) II and IV

248. XeF6 reacts with KF to give

(A) K[XeF6] (B) [XeF5]+[KF2]－
(C) [XeF4]2+[KF3]2－ (D) XeF4

249. Which of the following is not a target molecule for drug function in the body?

(A) Carbohydrate (B) Lipid
(C) Vitamins (D) Proteins

18

250. How do d orbits split in a square planar crystal field?

(A) dx 2  y2  dxy  dxz  dyz  dz 2
(B) dx 2  y2  dxy  dz 2  dxz  dyz
(C) dx 2  y2  dz 2  dxy  dxz  dyz
(D) dx 2  y2  dz 2  dxy  dxz  dyz

***

MATHEMATICS (UG) Final (Shift I)
(Corrected questions for image)

4. Two distinct polynomials f  x  and g  x  are defined by
f  x   x2  ax  2 and g  x   x2  2 x  a . If the equations f  x   0 and g  x   0 have
a common root then the sum of the roots of the equation f  x   0  g  x   0 is

1
(A)  (B) 0
2
1
(C) (D) 1
2

10. If the three points A 1,6  , B  3, 4  and C  x, y  are collinear, then the equation
satisfying by x and y is

(A) 5x  y  11  0 (B) 5 x  13 y  5  0
(C) 5 x  13 y  5  0 (D) 13x  5 y  5  0

13. From a circular disk of radius 13 cm a sector is cut with centre angle  . If the height of
the right circular cone formed using the above sector is 12 cm, then the  is

10 9
(A) (B)
13 13
5 6
(C) (D)
13 13

2n 2 n 1
15. If p and q are coefficients of xn in the expansions of 1  x  and 1  x 
p
respectively, then is equal to
q

(A) 4 (B) 1
(C) 9 (D) 2

18. There are 30 questions in a multiple choice test. A student gets 1 mark for each
unanswered question, 0 marks for each wrong answer and 4 marks for each correct
answer. A student answered x questions correctly and scored 60 marks. Then the
number of possible values of x is

(A) 15 (B) 10
(C) 6 (D) 5

26. Let I denote the 3 × 3 identity matrix and P be a matrix obtained by rearranging the
columns of I. Then

(A) there are six distinct choices for P and det  P   1
(B) there are six distinct choices for P and det  P   1
(C) there are more than one choices for P and some of them are not invetible
(D) there are more than one choices for P and P 1  I in each choice

33. Let R be the set of all real numbers and f :  1,1  R be defined by
 1
 x sin , x  0
f  x   x
 0, x0

(A) f satisfies the conditions of Rolle’s theorem on 1,1
(B) f satisfies the conditions of Lagrange’s Mean Value Theorem on 1,1
(C) f satisfies the conditions of Rolle’s theorem on  0,1
(D) f satisfies the conditions of Lagrange’s Mean Value Theorem on  0,1

 sin x 2
 when x  0;
46. Consider the function defined by f  x    x
 x 2  ax  b when x  0.

Suppose f  x  is differentiable on R, then

(A) a  0, b  0 (B) a  1, b  0
(C) a  0, b  1 (D) a  1, b  1

 x3 x 1
47. If f  x    2 where a, b and c are constants such that f  x  has second
ax  bx  c x  1
derivative at x  1 . Then a equals

(A) 6 (B) 3
(C) 6 (D) 3

48. A coin is tossed five times. If the outcomes are 2 heads and 3 tails (in same order), then
what is the possibility that the fourth toss is a head?

1 2
(A) (B)
4 5
1 3
(C) (D)
2 5

1 1
85. If f  x  . f    f  x   f   and f  4   65 , then f  6  is
 x  x

(A) 65 (B) 217
(C) 215 (D) 64

2
22  42  ...   2n 
102. For 2
to exceed 1.01, the maximum value of n is
12  32  ...   2n  1

(A) 99 (B) 100
(C) 101 (D) 150

2 1 4 5
109. The system of equations x  y  z  0, y  2 z  0, x  y  z  0 possesses
3 3 3 3

(A) no solution (B) only trivial solution
(C) infinite non-trivial solutions (D) one non-trivial solution

x  2 y 1 z  3
116. Coordinates of the points on the line   at a distance 5 units from the
3 2 2
point 1,3, 3 

 3, 7, 4   7, 4,3
(A) (B)
 2, 1,3  2, 1,3
 4,3, 7  1, 0,1
(C) (D)
 2, 1,3  2,1,3

117. Geetha and Somu appear for an interview for two vacancies in a company. The
1 1
probability of Geetha’s selection is and Somu is .
5 6
Then the probability that (i) both of them are selected (ii) both of them are not selected
are respectively

1 2 1 2
(A) , (B) ,
30 5 30 3

7 2 7 2
(C) , (D) ,
30 3 30 5

118. The set of homogenous equations
tx   t  1 y   t  1 z  0,  t  1 x  ty   t  2  z  0,  t  1 x   t  2  y  tz  0
has non-trivial solutions for

(A) three values of t (B) two values of t
(C) one value of t (D) no value of t

119. The points  0,8 / 3  , 1,3  and  82, 30 

(A) form an obtuse angled triangle
(B) form an acute angled triangle
(C) form a right angled triangle
(D) lie on a straight line
dy
122. The solution of the differential equation e dx  x  1 when y  0   3 is

(A) y  x log x  x  2 (B) y   x  1 log 1x  1  x  3
(C) y   x  1 log  x  1   x  3 (D) y  x log x  x  3

1 x x2
124. The equation x 2 1 x  0 has
x x2 1

(A) exactly two distinct roots (B) one pair of real equal roots
(C) three pairs of equal roots (D) modulus of each root is 2

125. n-similar balls each of weight 50 when weighed in pairs the sum of the weights of all
possible pairs is 120, when they are weighed in triplets the sum of the weights comes out
to be 480 for all possible triplets, then x is

(A) 5 (B) 10
(C) 15 (D) 20