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NDA MATH TEST-14

1. If A and B are finite sets, then n  A  B  is 10. cos 60 sin 240 cos 720 =
1 1 1 1
(a) n  A   n  B  (a) (b) (c) (d)
8 4 8 4
(b) n  A   n  B   n  A  B 
11. sin 200 sin 400 sin 800 =
(c) n  A   n  B   n  B  A 
3 3 3 3
(d) n  A   n  B   n  A  B  (a) (b) (c) (d)
4 8 4 2
2. If A = {4, 5, 8, 12}, B = {1, 4, 6, 9} and C = {1,
2, 3, 4}, then A – (B – A) is 12. If 1,1 ,  2 ,....... n 1 are the nth roots of unity
(a) A (b) B then 1  1 1   2  ... 1   n 1  
(c) 2A (d) 
(a) n  1 (b) n (c) -1 (d) 1
3. If X = {1, 2, 3, 4} and Y = {2, 4, 6, 8, 10, 12},
then which of the following is not a function? 4 n 1
1 i 
(a) {(1, 2), (2, 2), (3, 8), (4, 8)} 13.   =
(b) {(1, 10), (2, 6), (3, 6), (4, 10)} 1 i 
(c) {(1, 8), (2, 8), (3, 8), (4, 8)} (a) i (b) -i (c) 1 (d) -1
(d) {(1, 4), (2, 4), (4, 8)} 14. log  log i  =
1  x   2x 
4. If f  x   log  1  x  , then f  1  x 2  is  
    (a) log (b) log i
equal to 2 2
(a) 2f (x) (b) f (x)  i  
(c) log  (d) log i
1 x 2 2 2 2
(c) log x (d) log
1 x
1 i 
If If f  x   x , g  x   x  5 x  6 then
2 2 15. log  
5.  1 i 
g  2   g  3  g  0  i   
 (a)  (b) (c)  (d) i
f  0   f 1  f  2  2 2 2 2
a) 2 (b) 1 (c) 5/6 (d) 6/5 16. If  ,  are the roots of x -x+2=0 then 2

6. sin 1  sin 2  sin 3  3   3    3  .........

cos 1  cos 2  cos 3  (a) 6 (b) 6 (c) 10 (d) 3
(a) 0 (b) 1 (c) 2 (d) 3
17. If one root of the equation 5 x 2  13  k  0 is
7. 
Cot 1358  tan 3608 
0
  0
 the reciprocal of the other then
(a) -1 (b) 0 (c) 1 (d) 2 (a) k = 0 (b) k = 5 (c) k =1/6 (d) k=6
18. If the equations 2x 2  x  k  0 and
1  sin A
8.  x
1  sin A x2   1  0 have Common roots. then the
2
(a)  (sec A  tan A) value of k is.
(a) 1 (b) 3 (c) -1 (d) -2
(b)  (sec A  tan A)
19. If  ,  are the roots of x -x+1=0 then 2
(c)  (cos ecA  cot A)
(d)  (cos ecA  cot A) 5   5 
(a) 2 (b) 1 (c) 12 (d) 4
1  tan 2 30o
9.  1
1  tan 2 30o 20. The maximum value of is :
(a) 1 (b) 1/2 (c) 2 (d) 0 4x  2x 1
2

4 2 3
(a) (b) (c) 1 (d)
3 3 4
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5  2x x 36. The centre of the circle passing through the
21. The solution of   5, x  R is points( h,0), (k,0), (0,h), (0,k) is
3 6
(a) x > 8 (b) x  8 (c) x < 8 (d) x  8 h h k k
22. If nP7 = 42 nP5 then n = (a)  ,  (b)  , 
2 2 2 2
(a) 5 (b) -1 (c) 7 (d) 12
hk hk h h
23. If 12Pr = 1320 then r = (c)  ,  (d)  , 
(a) 2 (b) 3 (c) 4 (d) 5  2 2  2 2
24. 2n n
If C3 : C2 = 44 : 3 then n = 37. If the points (0,0),(2,0),(0,4),(1,k) are concyclic
(a) 6 (b) 7 (c) 8 (d) 9 then k2 - 4k =
25. If nC3 = nC9 then nC2 = (a) -1 (b) 1 (c) 0 (d) -3
(a) 66 (b) 132 (c) 72 (d) 98 38. The locus of the centre of a circle passing
5
through a point and touching a line is
 3
26. The 5th term in the expansion of  2x 2   is (a) a straight line (b) an ellipse
 x
(c) a parabola (d) a hyperbola
(a) 810.x-2 (b) 810.x-4
(c) 810 (d) 810.x-5 39. The focus and vertex of a parabola are (4, 5)
and (3, 6). The equation of axis is
27. 1  2 6  (a) 2x-y+3=0 (b) 2x-y=0
(c) 2x+y-13=0 (d) x+y-9=0
(a) 98  70 2 (b) 99  70 2
40. If the parabola y 2  4ax passes through (-3, 2)
(c) 99  70 2 (d) 98  70 2 then the length of its latusrectum is
28.  3 1  5  3 1  5 (a)
2
3
(b)
1
3
(c)
4
3
(d) 4
(a) 152 (b) 142 (c) 124 (d) 162
41. Equation of the parabola having focus (3, 2)
and vertex (-1, 2) is
29. The sequence is
(a)  x  1  16  y  2  (b)  x  1  16  y  2 
2 2

(a) H.P. (b) G.P.

(c)  y  2   16  x  1 (d)  y  2   16  x  1
2 2
(c) A.P. (d) None of these
30. If the 9th term of an A.P. be zero, then the ratio 42. The number of normals that can be drawn from
of its 29th and 19th term is a point to the ellipse is
(a) 1 : 2 (b) 2 : 1 (c) 1 : 3 (d) 3 : 1 (a) 1 (b) 2 (c) 3 (d) 4
31. If the term of an A.P. be q and term be 43. The eccentricity of the Ellipse 9x2 + 16y2 =
p, then its rth term will be 576 is
(a)   (b)   7 5 77
(c)   (d)   (a) (b) (c) (d)
2 4 12
4
32. If   are in A.P. then 7th term of 44. The eccentricity of the ellipse 5x2+9y2= 1 is
the series is
2 3 4 1
(a)  (b) – 33 (a) (b) (c) (d)
(c) 33 (d) 10 a – 4
3 4 5 2
33. The inclination of a line is 15O. Its slope is 45. Equation of the hyperbola with foci 0, 5 and
5
(a) 3 1 (b) 1  3 e is
3
(c) 3  2 3 (d) 2  3 x 2 y2 x 2 y2
(a)  1 (b)   1
34. If  is an acute angle between the lines 9 16 16 9

y=2x+3, y=x+1 then the value of tan  = x 2 y2 x 2 y2

(c)  1 (d)  1
16 9 12 13
2 1 3 1
(a) (b) (c) (d) 5
3 3 4 2 46. The eccentricity of a hyperbola is then the
3
35. If the distance between the lines 2x+y+k=0, eccentricity of the conjugate hyperbola is
7 5 7 7 5
6x+3y+2=0 is then the value of k is (a) (b) (c) (d)
3 5 2 2 3 4
(a) 5 (b) 3 (c) 6 (d) 7
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47. The domain of sin-1x is 58. If the system of equations x + y + z = 6, x + 2y
+ z = 0, x + 2y + 3z = 10 has no solution, then
(a)   ,   (b)  1,1
=
(c)  0, 2  (d)  ,   (a) 2 (b) 3 (c) 4 (d) 5

 5  sin x
cot 1  cot 59. L im 
48. = x 0
x2
 6 
(a) 1 (b) -1 (c) 0 (d) doesn’t exist
5 3  
(a) (b) (c) – (d) sin 3 x tan 4 x
6 6 6 6 60. L im =
x 0 x sin 5 x
7
49. sin(Tan-1 )= 5 12
24 (a) 1 (b) (c) 0 (d)
12 5
(a) 24/25 (b) 7/25 (c) 7/24 (d) 25/24
log 1  ax   log 1  bx 
12 13  61. L im 
50. If Sin (
-1
) + Sec (-1
)= then x = x 0 x
13 x 2
(a) a  b (b) a  b
(a) 12 (b) 13 (c) 11 (d) 5
51. (Adj AT) = (c)   a  b  (d) ab
(a) (Adj A)T (b) Adj A
Lim 
 x  1  2 x  3 
(c) AT (d) Adj[A]1 62.  =
x 
 x  2  3x  4 
52. If Tr (A) = 2 + i  Tr[ (2-i) A] =
(a) 2 + i (b) 2 - i (c) 3 (d) 5 2 1 1
(a) (b) 0 (c) (d)
2 0 0 3 3 4
0 2 0  x tan 2 x
53. If A =  , then A4 = .... 63. The function f(x)= for x  0,
 0 0 2  sin 3x. sin 5 x
(a) 16A (b) 32 I (c) 4A (d) 8A = k for x=0, is continuos at x=0, then f(0)
54. If A and B are two matrices such that A + B 2 2 2 2
and AB are both defined then (a) (b) (c) (d)
13 17 11 15
(a) A and B are two matrices not necessarily
64. The value of f(0) for the function f(x) =
of same order
(b) A and B are square matrices of same order e x  e x
(c) A and B are matrices of same type so that it is continuous everywhere is
x
(d) A and B are rectangular matrices of same (a) 1 (b) 1/2 (c) 2 (d) 0
order
d  log 1 cot 2 x 
a b c 65. e =
dx  
If A  b c a (a) cosecx cotx (b) -cosecx.cotx
55. then cofactor of a21 is
c a b (c) cosec2x.cotx (d) 0
d  1 x  1 x  1 
(a) b2 - ac (b) ac - b2 (c) a2-bc (d) bc-a2 66. sec  sin 1 =
dx  x 1 x  1 
1990 1991 1992  (a) -1 (b) 0 (c) 1 (d) 2
1991 1992 1993 1
56. det  = 67. The derivative of esin x w.r.t. logx is
1992 1993 1994 
1 1
 xesin x xesin x
(a) 1992 (b) 1993 (c) 1994 (d) 0 (a) (b)
57. If the value of a third order determinant is 11, 1  x2 1  x2
then the value of the determinant of A1  1
esin x
1
(a) 11 (b) 121 (c) 1/11 (d) 1/121 (c) (d) esin x . 1  x 2
1  x2

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1  sin 2 x  dy  78. In a circle of radius 'r' units, the rate of change
68. If y= then   =
1  sin 2 x  dx  x 0 of area of a sector is
(a) Directly proportional to the rate of change
1
(a) (b) 1 (c) -2 (d) 2 of the angle.
2 (b) Inversely proportional to the rate of change
d of the angle of the sector
69. {log10(sin-1x2)}=
dx (c) A constant
1 (d) Directly proportional to the radius
(a)
 Sec
1 2
log10 .(sin x ). 1  x 4 79.
2
x.Co sec 2 x dx 
2x (a) tan x - cot x + c (b) tan x + cot x + c
(b) log10 .(sin 1 x 2 ). 1  x 4 (c) tan x cot x + c (d) Sec x tan x + c
1 sin x  Cos x
(c)
log10 .(sin 1 2
x ). 1  x 4 80.  1  sin 2 x
dx 
2
(d) 1 2
(a) x  c (b)  x  c
log10 .(sin x ). 1  x 4
2
(c) sin x  cos x  c (d) x  c
1 1  x
70. The derivative of Cos w.r.t. Sec2 x
1 x2 81.  (1 tan x)3 dx 
1 2x
Tan is 1 1
1 x2 (a)  c (b) c
2(1  tan x ) 3
(1  tan x) 3
1
(a) 0 (b) 1 (c) 2 (d) 1 1
2  c (d) c
(c)
71. f(x)=x3 - 27x + 5 is monotonically increasing (1  tan x) 2
2(1  tan x ) 2
for
e x (1  x)
(a) x < -3 (b) >3 82.  Sin 2 ( xe x ) dx 
(c) <3 (d) x > 3 (a) tan (xex) + c (b) - cot(xex) + c
72. The diagonal of the rectangle of maximum (c) sin (xex) + c (d) sin ex + c
area having perimeter 100 cm is 
sin   cos 
(a) (b) 10 (c) (d) 15 83.  1  sin 2
d =
73. The absolute minimum of y = c cosh x/c is 0

(a) 1/c (b) c/2 (c) c (d) 2c (a)  (b)  +  and  >0
74. The slope of the normal to the curve given by (c)  /2 (d)  /3
 84. =
x  a(  sin ), y  a(1  cos ) at  2a
f ( x )dx
1 1
2
0 f ( x )  f (2a  x )
(a) (b) (c) –1 (d) 2
2 2 (a) a (b) a/2 (c) 0 (d) 2a
75. The point on the curve y  x 2  4x  5 at 
which the tangent drawn is parallel to x-axis is 2
4
(a) (0, 5) (b) (1, 2) (c) (2, 1) (d) (3, 2) 85.  sin xdx =
0
76. If the curves ay  x 2  7 and x 3  y cut
 3 3
orthogonally at (1, 1) then a = (a) (b) (c) (d) 0
12 7 16
1
(a) 1 (b) – 6 (c) 6 (d) 86. The area between the curve y 2  9 x and
6
77. The velocity v of a particle moving along a the line y  3x is
straight line when it is at a distance X from the 1 8
point of start is given by a+bv2=x2, then the (a) sq. units (b) sq. units
acceleration is 3 3
X X b b2
1 1
(a) (b) (c) (d) (c) sq, units (d) sq. units
b b2 X X 2 5
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87. The area bounded by the ellipse 97. Two cards are drawn from a pack of 52 cards.
Find the probaility of getting both the Aces?
3 x  2 y  6 with the co-ordinate axes in
2 2
(a) 1/26 (b) 1/2 (c) 1/221 (d) None
sq. units is
98. The probability that a leap year selected at
(a) 6 (b) 8 (c) 12 (d) 3 random will contain 53 sunday is :
88. The number of arbitarary constants in the so- (a) 1/7 (b) 2/7 (c) 2/366 (d) 3/366.
lution of a differential equation of degree 3 and 99. If mean of x and 1
x is m, then mean of x2 and
order 2 is 1
(a) 2 (b) 3 (c) 5 (d) 1 is :
x2
(a) m2 (b) m2/4
89. I.F of 1  x  dy
3

dx
 3x 2
y  sin 2 x (c) 2m - 1
2
(d) 2m2 + 1.
100. The mean of a set of observation is x. If each
1 1 observation is divided by  , and then is
(a) 1  x 3 (b) (c) 3x 2 (d) increased by 10, then the mean of new set is -
1  x3 x3
(a) x/  (b) (x + 10)/ 
dy (c) (x + 10  )/  (d) x + 10.
90. The solution of  y  sin x
dx 101. If the pth term of an A.P. is q and the qth term is
p, then the rth term is
ex
(a) ye 
x
sin x  cos x  c (a) q - p + r (b) p - q + r
2 (c) p + q + r (d) p + q - r.
ex 102. The fourth term of an A.P. is 4, then the sum of
(b) e y 
x
cos x  sin x   C first sevent terms is
2
(a) 4 (b) 28
(c) y  e
x
 sin x  cos x   c (c) 16 (d) 40
(d) y  e x  sin x  cos x   c 103. The first and last terms of an A.P. are 1 and 11.
If the sum of its terms is 36, then number of
91. If  =3i-2j+k,  = -i+j+k then the unit vector terms will be
parallel to the vector (   ) is (a) 5 (b) 6
(a) (2/3)i -(1/3)j+(2/3)k (c) 7 (d) 8.
(b) (2/5)i -(1/5)j+(2/5)k 104. The third term of an A.P. is 7 & its 7th terms is 2
more than thrice of its 3rd term, then the sum of
(c) ( 2 / 3 ) i  (1 / 3 ) j  (2 / 3 )k
first 20 terms is
(d)  (2 / 3 ) i  (1 / 3 ) j  (2 / 3 )k (a) 640 (b) 740
92. If a and b be two unit vectors and a+b is also (c) 74 (d) 700.
a unit vector then (a,b)= 105. A student reads common difference of an A.P.
(a)  / 4 (b)  / 3 (c) 2 / 3 (d)  / 2 as -2 instead of 2 and got the sum of first five
93. The perpenducular distance from origin to the terms as -5. The actual sum of first five terms is
plane 3x - 2y - 2z = 2 (a) 25 (b) -25
(c) 35 (d) -35.
(a) 1 / 17 (b) 2 / 17
106. If in an infinite G.P., first term is equal to 10 times
(c) 3 / 17 (d) 4 / 17 the sum of all successive terms, then the common
94. The work done by the force F=2i-3j-2k in ratio is
moving a particle from(3,-2,5) to (1,-4,3) is (a) 1/9 (b) 1/10
(a) -2 (b) -3 (c) -4 (d) 6 (c) 1/11 (d) None
95. The number of points equidistant from two 107. The sum to infinity of the series
given points is 1+4/5 + 7/52 + 10/53 + ..... is -
(a) 0 (b) 1 (c) 2 (d) Infinite (a) 35/16 (b) 1/8
96. A = (1, -1, 2) and B = (2, 3, 7) are two points. If (c) 16/35 (d) None of these.
P, Q divide AB in the ratios 2 : 3, -2 : 3
108. The sum of the numbers 1, 8, 27 .......,1000 is
respectively then Px  Q y  (a) 385 (b) 381
38 38 2 47 (c) 3125 (d) None of these.
(a) (b) (c) (d)
5 5 5 6

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109. 113 + 123 + 133 + ..... + 203 is 116. If A is a matrix of 4x3 and B is a matrix of order
(a) 40075 (b) 41075 3x5 and C is a matrix of 5x4, then the number of
(c) 42075 (d) None of these. entries in AxBxC is equal to
110. The nth term of the series 7+77+777+ ........ is- (a) 12 (b) 15
(a) 7 x 10n-1 (b) 7 x 11n-1 (c) 16 (d) 20.
(c) 7/9 (10 )
n-1
(d) None of these 117. If a mastrix has 13 elements, then the possbile
dimensions (order) it can have are
111. The foot of the perpendicular from the point
(a) 1×13, 13×1 (b) 1×26, 26×1
(2, 4) upon x + y = 1 is
(c) 2×13, 13×2 (d) None of these
1 3  1 3  118. If AB=A, BA=B, then A = 2
(a)  2 , 2  (b)   2 , 2 
    (a) I (b) A
4 1 3 1 (c) B (d) None
(c)  3 , 2  (d)  4 ,  2 
  
112. Three lines 3x - y = 2, 5x + ay = 3 and

LM1 -1 OP LM
, B=
a 1 OP
, (A+B)2 =A2+B2,
2 x + y = 3 are concurrent, then a
119. If A =
N2 -1 Q N b -1 Q
(a) 2 (b) 3 then a =
(c) -1 d) -2 (a) -1 (b) 1
(c) 4 (d) -4.
( a  h )2 sin(a  h) – a 2 sin a
113. lim
h0 h

120. If A =
LM0 1OP
, then A4 =
(a) a2cos a + a sin a (b) a2 cos a + 2a sin a N1 0 Q
(c) 2a2 cos a + a sin a (d) none of these
114. The integrating factor of the different equation
LM1 0OP LM1 1 OP
dy
( x log x )  y  2 log x is given by
(a)
N0 1 Q (b)
N0 0 Q
dx
(c) M
L0 0O L0 1O
1 PQ
(d) M
0PQ
(a) ex (b) log x
(c) log(log x) (d) x N1 N1 .

115. The angle between the lines 2x - y + 3 = 0

and x + 2y + 3 = 0 is
(a) 90° (b) 60°
(c) 450 (d) 30°

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 NDA MATH TEST-14 ANSWER KEY
1 D 26 A 51 A 76 C 101 D
2 A 27 B 52 D 77 A 102 B
3 D 28 A 53 D 78 A 103 B
4 A 29 C 54 B 79 A 104 B
5 D 30 B 55 B 80 D 105 C
6 A 31 B 56 D 81 D 106 D
7 B 32 A 57 C 82 B 107 A
8 A 33 D 58 B 83 C 108 D
9 B 34 B 59 D 84 A 109 B
10 C 35 B 60 D 85 C 110 D
11 B 36 C 61 B 86 C 111 B
12 B 37 B 62 A 87 A 112 D
13 A 38 C 63 D 88 A 113 B
14 C 39 D 64 C 89 A 114 B
15 D 40 C 65 B 90 A 115 A
16 A 41 C 66 B 91 A 116 C
17 B 42 D 67 B 92 C 117 A
18 D 43 D 68 C 93 B 118 B
19 B 44 A 69 B 94 D 119 B
20 A 45 B 70 B 95 D 120 A
21 B 46 D 71 B 96 A
22 D 47 B 72 C 97 C
23 B 48 A 73 C 98 B
24 A 49 B 74 C 99 C
25 A 50 A 75 C 100 C