2. SECTION – I
Single Correct Answer Type
There are five parts in this question. Four choices are given for each part and one of them is
correct. Indicate you choice of the correct answer for each part in your answer-book by
writing the letter (a), (b), (c) or (d) whichever is appropriate
3. 01 Problem
The value of 2 2 2 .... is equal to :
a. 5
b. 3
c. 2
d. none of these
4. 02 Problem
If 3x – 3x-1 = 6, then xx is equal to :
a. 2
b. 4
c. 9
d. none of these
5. 03 Problem
a b a b
The determinant is equal to zero, if a, b, c are in :
b c b c
2 1 0
a. GP
b. AP
c. HP
d. None of these
6. 04 Problem
3n 3n
2 2
The value of 1 2 1 2 is :
a. Zero
b. 1
c. ω
d. ω2
7. 05 Problem
The value of i1/3 is :
3 i
a. 2
3 i
b.
2
c. 1 i 3
2
1 i 3
d.
2
8. 06 Problem
n
Least value of n for which 1 i 3 is an integer, is :
1 i 3
a. 1
b. 2
c. 3
d. 4
9. 07 Problem
2 6
If A = 5 7
, then adj (A) is equal to :
7 6
a. 5 2
2 6
b. 5 7
7 5
c.
6 2
d. none of these
10. 08 Problem
1 x2 x3 1 2 x4 x6
If sin x ... cos x ... for 1 | x | 2 , then
2 4 2 4 2
the value of x is :
a. 1/2
b. 1
c. -1/2
d. none of these
11. 09 Problem
If I /2 cos x
dx , then the value of I is equal to :
0
sin x cos x
a.
2
b. 4
c.
6
d. none of these
12. 10 Problem
If sin cosec =2, then sinn cosecn is equal to :
a. 2
b. 2n
c. 2n-1
d. none of these
13. 11 Problem
2 4 8
If the sum of the series 1 ... is a finite number, then :
x x2 x3
a. x < 2
b. x > 2
c. x >
d. none of these
14. 12 Problem
1 1 1
The sum of n terms of the series 1 3 3 5 5 7
….. is equal to :
a. 2n 1
2n 1
b. 2
c. 2n 1 1
2n 1 1
d.
2
15. 13 Problem
A person traveling with a velocity v1 for some time and with uniform velocity v2
for the next equal time. The average velocity v’ is given by :
a. v' = v1 v2
2
b. v ' v1v2
2 1 1
c. v' v1 v2
1 1 1
d. v ' v1 v2
16. 14 Problem
In the binomial expansion (a + bx)-3 = x + ….., then the value of a and b are :
a. a = 2, b = 3
b. a = 2, b = -6
c. a = 3, b = 2
d. a = -3, b = 2
17. 15 Problem
2 2
ax a x
ax a x
1
2 2
The value of determinant bx b x
bx b x
1 , is :
2 2
x
c c cx c x
1
a. 0
b. 2 abc
c. a2b2c2
d. none of these
18. 16 Problem
If one root of the equation x2 + px + q = 0 is 2 + , then values of p and q are :
a. - 4, 1
b. 4, -1
c. 2, 3
d. - 2, - 3
19. 17 Problem
x2 14x 9
If x is real, then value of the expression 2 lies between :
x 2x 3
a. 5 and 4
b. 5 and – 4
c. -5 and 4
d. none of these
20. 18 Problem
10
x 3
The coefficient of x4 in the expansion of is equal to :
2 x2
405
a.
256
504
b. 263
450
c. 263
d. none of these
21. 19 Problem
2 tan-1 (cos x) = tan-1 (cosec2 x), then x is equal to :
a.
2
b. π
c. 6
d. 3
22. 20 Problem
Period of sin2 x is equal to :
a. π
b. 2 π
c. π/2
d. none of these
23. 21 Problem
If 2 1 sin xdx 4cos ax b c , then the value of (a, b) is equal to :
1
a. ,
2 4
b. 1
2
c. 1,1
d. none of these
24. 22 Problem
Among 15 players, 8 are batsmen and 7 are bowlers. The probability
that a team is chosen of 6 batsmen and 6 bowlers, is :
8
C6 x 7C5
a. 15
C11
28
b.
15
15
c.
28
d. none of these
25. 23 Problem
In the expansion of (1 + x)n, coefficients of 2nd, 3rd and 4th terms are in AP. Then, n
is equal to :
a. 7
b. 9
c. 11
d. none of these
26. 24 Problem
3 /2
2
The degree and order of the equation dy d2y is :
1 k
dx dx 2
a. (2, 2)
b. (3, 2)
c. (2, 3)
d. none of these
27. 25 Problem
If a and b are two unit vectors inclined at as angleѲ , then sin Ѳ/2 is equal to :
a. 1
b. 1/2
c. - 1/2
d. none of these
28. 26 Problem
a b c
If , , are in HP, then :
b c a
a. a2b, c2a, b2c are in AP
b. a2b, b2c, c2a are in HP
c. a2b, b2c, c2a are in GP
d. none of the above
29. 27 Problem
a b ax b /x
If b c bx c = 0, then a, b, c are in :
ax b bx c 0
a. AP
b. GP
c. HP
d. None of these
30. 28 Problem
If x2 – 5x + 6 > 0, then x :
a. ,2 3,
b. [2, 3]
c. (2, 3]
d. none of these
31. 29 Problem
If x > 0 and x 1, y > 0 and y 1, z > 0 and z 1, then the value of
1 logx y logx z
is equal to :
logy x 1 logy z
logz x logz y 1
a. 1
b. -1
c. zero
d. none of these
32. 30 Problem
3 2 4
If matrix 1 1 adj (A), then k is equal to :
A 1 2 1 and A
k
0 1 1
a. 7
b. -7
c. 15
d. 11
33. 31 Problem
The projection of the vector i j ˆ
ˆ 2ˆ k on the vector i j ˆ
4ˆ 4ˆ 7k is equal to :
a. 5 6
10
19
b.
9
9
c.
19
6
d. 19
34. 32 Problem
If a 2i j ˆ
ˆ 4ˆ 5k and b i j ˆ
ˆ 2ˆ 3k, then| a x b | is equal to :
a. 11 5
b. 11 3
c. 11 7
d. 11 2
35. 33 Problem
the area of the parallelogram whose diagonals are is equal to :
a. 5 3
b. 5 2
c. 25 3
d. 25 2
36. 34 Problem
1
The most general solution of tan 1 and cos is :
2
7
a. n
4
7
b. n ( 1)n
4
7
c. 2n
4
d. none of these
37. 35 Problem
x tan x dx
The value of dx is equal to :
0 sec x cos x
2
a. 4
2
b.
2
3 2
c.
2
2
d.
3
38. 36 Problem
x ex ex ......... dy
If y e , is equal to :
dx
x
a. 1 x
y
b. 1 y
y
c. y 1
1 y
d. y
39. 37 Problem
cos2x3 1 is equal to :
lim
x 0 sin6 2x
1
a.
16
1
b. - 16
1
c. 32
1
d. - 32
40. 38 Problem
d2 y
If x a sin and y b cos , then 2 is equal to :
dx
a
a. 2
sec2
b
b
b. sec2
a
b
c. 2
sec3
a
b
sec3
d. a2
41. 39 Problem
Differential equation of y = sec (tan-1 x) is :
a. (1 + x2) dy =y+x
dx
dy
b. (1 + x2) dx
=y–x
dy
c. (1 + x2) dx = xy
dy x
d. (1 + x 2) = y
dx
42. 40 Problem
If ‘H’ is the harmonic mean between P and Q, then H H is :
P Q
a. 2
PQ
b.
P Q
c. P Q
PQ
d. none of these
43. 41 Problem
If tan3x tan2x 1, then x is equal to :
1 tan3x tan2x
a.
b. 4
c. n ,n 1, 2, 3,...
4
d. 2n ,n 1, 2, 3,...
4
44. 42 Problem
The value of 2(sin6 θ + cos6 θ ) –3(sin4 θ + cos4 θ) + 1 is equal to :
a. 2
b. zero
c. 4
d. 6
45. 43 Problem
/4
If un = tann d , then un un 2
is equal to :
0
1
a. n 1
b. 1
n 1
c. 1
2n 1
1
d. 2n 1
46. 44 Problem
The equation of the normal to the hyperbola x2 y2
1 at (-4, 0) is :
16 9
a. y = 0
b. y = x
c. x = 0
d. x = -y
47. 45 Problem
x dx is equal to :
1 x4
a. log (1 + x2) + c
b. tan-1 x2 + c
1
c. 2 tan-1 x2 + c
d. none of these
48. 46 Problem
2 3
The value of a b 1 a b 1 a b
....
a 2 a 3 a
b
a. log a
b. log a – log b
c. log a + log b
d. none of these
49. 47 Problem
If y = a log x + bx2 + x has its extremum value at x = 1 and x = 2, then (a, b) is :
1
a. 1,
2
1
b. ,2
2
c. 1
2,
2
2 1
d. ,
3 6
50. 48 Problem
y2 + xy + Px2 – x – 2y + P = 0 represent two straight lines, if P is equal to :
a. 2
b. 2/3
c. 1/4
d. 1/2
51. 49 Problem
af (x) xf (a)
If f(x) is a differentiable function, then lim is equal to :
x a x a
a. af'(a) – f(a)
b. af(a) – f’(a)
c. af’(a) + f(a)
d. af(a) – f’(a)
52. 50 Problem
If z = x + iy, then the area of a triangle with vertices z, iz and z + iz is equal to :
3
a. 2
|z|2
b. |z|2
1
c. 2
|z|2
1
d. 4 |z|2
53. 51 Problem
If sets A and B are defined as A {(x, y); y ex , x R}B {(x, y); y x, x R}
, then :
a. B A
b. A B
c. A B
d. A B A
54. 52 Problem
Number of way in which 7 mean and 7 women can sit on a round table such that
no two women sit together are :
a. (7!)2
b. 7! X 6!
c. (6!)2
d. 7!
55. 53 Problem
Let a and b be two equal vectors inclined at an angleθ , then sin θ /1 is equal to :
1
|a b|
a. 2
| a|
1
|a b|
b. 2
| a|
c. |a b|
d. | a b|
56. 54 Problem
The angle of intersection between the curves x2 = 4(y +1) and x2 = - 4(y +1) is :
a. π/6
b. π/4
c. Zero
d. π/2
57. 55 Problem
If a, b, c are three vectors such that | a | 3,| b | 4,| c | 5,| a b c | 0, then the
value of a b b c c a is equal to :
a. -20
b. -25
c. 25
d. 50
58. 56 Problem
9
The value of [ x 2]dx where [.] is the greatest integer function :
0
a. 31
b. 22
c. 23
d. none of these
59. 57 Problem
1 is :
limcos
x 0 x
a. continuous at x = 0
b. differentiable at x = 0
c. does not exist
d. none of the above
60. 58 Problem
The work done by the force F i j ˆ
ˆ 2ˆ 4k in displacing an object from
ˆ
ˆ 5ˆ 3k to r2 ˆ
r1 i j 3ˆ 8ˆ 5k
i j is equal to :
a. 0 unit
b. 20 unit
c. 15 unit
d. none of these
61. 59 Problem
Equation 3x2 + 7xy + 2y2 + 5x + 5y + 2 = 0 represents :
a. a pair of straight lines
b. an ellipse
c. a hyperbola
d. none of the above
62. 60 Problem
If an angle divided into two parts A and B such that A – B = K and tan A : tan B =
k: 1, then the value of sin k is :
k 1
a. sin
k 1
k
b. sin
k 1
k 1
c. sin
k 1
d. none of these
63. 61 Problem
Which is true about matrix multiplication :
a. It is commutative
b. It is associative
c. Both a and b
d. None of these
64. 62 Problem
Inverse of the function, y = 2x – 3 is equal to :
a. x 3
2
b. x 3
2
1
c.
2x 3
d.none of these
65. 63 Problem
In a right angled triangle, the hypotenuse is four times as long as the
perpendicular to it from the opposite vertex, one of the acute angles is :
a. 150
b. 300
c. 450
d. none of these
66. 64 Problem
Angle between two curves x2 = 4(y + 1) and x2 = - 4(y +1) is :
a. 0
b. 900
c. 600
d. 300
67. 65 Problem
1
If the binomial expansion of (a + bx)-2 is - 3x + …, then (a, b) is equal to :
4
(2, 12)
(2, 8)
(-2, -12)
none of these
68. 66 Problem
The range of a projectile fixed at an angle of 150 is 50 m. If it is fixed with the
same speed at an angle of 450, then the range will be :
a. 50 m
b. 100 m
c. 150 m
d. none of these
69. 67 Problem
1 0 k
Matrix A = 2 1 3 is not invertible for :
k 0 1
a. k = 2
b. k = 2
c. k = 0
d. all real values of k
70. 68 Problem
1 1
If A , then A100 is equal to :
1 1
a. 2100 A
b. 299 A
c. 2101 A
d. none of these
71. 69 Problem
The probability that the two digit number formed by digits 1, 2, 3, 4, 5 is divisible
by 4, is
a. 1/30
b. 1/20
c. 1/5
d. none of these
72. 70 Problem
Let f (x y) f (x)f (y ) x, y R, f(5) = 2, f’(0) = 3, then f’(5) equals :
a. 4
b. 1
c. 1/2
d. 6
73. 71 Problem
A particle is projected down from the top of tower 5 m high and at the same
moment another particle is projected upward from the bottom of the tower with
a speed of 10 m/s, meet at a distance ‘h’ from the top of tower, then h is equal to
:
a. 1.25 m
b. 2.5 m
c. 3 m
d. none of these
74. 72 Problem
If a couple is acting on two particles of mass 1 kg attached with a rigid rod of
length 4 m, fixed at centre acting at the end and the angular acceleration of
system about centre is 1 rad/s2 , then magnitude of force is equal to :
a. 2N
b. 4 N
c. 1 N
d. none of these
75. 73 Problem
The integral factor of expansion (x2 + 1) + 2xy = x2 –1, is :
a. x2 +1
2x
b. 2
x 1
x2 1
c.
x2 1
d. none of these
76. 74 Problem
From a pack of cards, 2 cards are drawn at random one by one with replacement.
The probability that the first is heart and second is king, is equal to :
a. 1/26
b. 1/52
c. 1/13
d. 1/10
77. 75 Problem
Eccentricity of the curve x2 – y2 = a2 is equal to :
a. 2
b. 2
c. 4
d. none of these
78. 76 Problem
A weight of 10 N is hanged by two ropes as shown in figure, tensions T1 and T2
are :
image*
a. 5N, 5 3 N
b. 5 3 N, 5N
c. 5N, 5N
d. 5 3 N, 5 3 N
79. 77 Problem
Let A and B be two events such that P (A) = 0.3, P( A B ) = 0.8. If A and B are
independent events, then P(B) is equal to :
5
a.
7
5
b. 13
1
c.
3
1
d.
2
80. 78 Problem
Two masses are attached to the pulley as shown in figure. Acceleration of centre
of mass is :
a. g/4
b. - g/4
c. g/2
d. - g/2
81. 79 Problem
A particle is thrown with velocity u at an angle of 300 from horizontal line. It
bcomes perpendicular to its original position at time :
u
a. 2g
b. 2ug
c. u 3
g
d. none of these
82. 80 Problem
In the following, one-one function is :
a. ex
2
b. e x
c. sin x
d. none of these
83. 81 Problem
The value of (ex - 1) is always :
a. Greater than 1 for all real values
b. Less than 1 for all real values
c. Greater than 1 for some real values
d. None of the above
84. 82 Problem
If the force represented by 3ˆ
j ˆ
2k is acting through the point 5ˆ
i j ˆ
4ˆ 3k , then
its moment about the point (1, 3, 1) is :
a. i j ˆ
14ˆ 8ˆ 12k
b. i j ˆ
14ˆ 8ˆ 12k
ˆ
6ˆ ˆ 9k
i j
c.
d. 6ˆ
i j ˆ
ˆ 9k
85. 83 Problem
8
Coefficient of x2 in the expansion of X 1 is equal to :
2x
a. 1/7
b. -1/7
c. -7
d. 7
86. 84 Problem
0 3
If A and A 1
A , then is equal to :
2 0
1
a. - 6
1
b. 3
1
c. - 3
1
d. 6
87. 85 Problem
1 x x2
Minimum value of for al real ‘x’ is equal to :
1 x x2
a. Zero
b. 1/3
c. 1
d. 3
88. 86 Problem
[ˆ ˆ] [kji ] [ˆˆ ]
ˆ
ikj ˆˆ
ˆ ˆ
jki is equal to :
a. -1
b. 3
c. -3
d. -2
89. 87 Problem
If x, 2x + 2, 3x + 3 are in GP, then the fourth term is :
a. 27
b. -27
c. 13.5
d. -13.5
90. 88 Problem
If nC12 = nCB, then n is equal to :
a. 20
b. 12
c. 6
d. 30
91. 89 Problem
1 2 1 4 0 1
If A ,B and C , then 5A – 3B + 2C is equal to :
3 0 2 3 1 0
8 20
a. 7 9
8 20
b. 7 9
8 20
c. 7 9
8 7
d. 20 9
92. 90 Problem
11 12 13 is equal to :
12 13 14
13 14 15
a. 1
b. zero
c. -1
d. 67
93. 91 Problem
x 1 x 1 dy
If y sec 1
x 1
sin 1
x
,
1 dx
is equal to :
a. 1
x 1
b. x 1
c. zero
x 1
d. x 1
94. 92 Problem
If sin y = x sin (a + y), then dy is equal to :
dx
sin a
a.
sin a sin2 a y
sin2 a y
b.
sin a
c. sin a sin2 (a + y)
sin2 a y
d. sin a
95. 93 Problem
The two curves x3 – 3xy2 +2 = 0 and 3x2 – y3 = 2 :
a. Cut at right angle
b. Touch each other
c. Cut at an angle π/3
d. Cut at an angle π/4
96. 94 Problem
dx is equal to :
3/4
2 4
x x 1
1/4
a. 1
1 c
x4
b .(x4 + 1)1/4 + c
1/4
1
c. 1 c
x4
1/4
d. - 1
1 c
x4
97. 95 Problem
The value of the integral is :
a. Zero
b. 1/2
c. -1/2
d. none of these
98. 96 Problem
A fair coin is tossed repeatedly. If tail appears on first four tosses, then the
probability of head appearing on fifth toss equals :
a. 1/2
b. 1/32
c. 31/32
d. 1/5
99. 97 Problem
There are four machines and it is known that exactly two of them are faulty. They
are tested one in a random order till both the faulty machines are identified.
Then, the probability that only two tests are needed, is ;
a. 1/3
b. 1/6
c. 1/2
d. 1/4
100. 98 Problem
If fifth term of an GP is 2, then the product of its 9 terms is :
a. 256
b. 512
c. 1024
d. none of these
101. 99 Problem
If p and q are the roots of the equation x2 + px + q = 0, then :
a. p = 1
b. p = 0 or 1
c. p = - 2
d. p= - 2 or zero
102. 100 Problem
Let A and B be two finite sets having m and n elements respectively. Then, the
total number of mappings from A to B is :
a. mn
b. 2mn
c. mn
d. nm
