OURS ACADEMY

 e 5 log x  e 4 log x   1 t2 
1.   e3log x  e 2 log x dx = 9. The area bounded by the curve x  a  1  t 2  ,
 
x3 x3 2at
(a) x + c (b) 3x2+c (c)  c (d) c y in sq. units is
3 2 1 t2
x  a2  a2 3 a 2
2.  x dx = (a)
2
(b)  a 2 (c)
4
(d)
2
(a) x  c (b) - x  c (c) |x| + c (d) x2 + c 10. The order and degree of the differential equation
of rectangular hyperbola is
e x 1  x e 1
3.  e x  x e dx  11.
(a) 2,2 (b) 3,2 (c) 1,2 (d) 1,1
The D.E whose solution is y  c sin x is
1 dy
(b) log e  x  c
x e
(a) log|ex+xe|+c (a)  y cot x (b) y2  y  0
e dx
1 dy dy
(c)  log e  x  c
x e
(d)  log e  x  c
x e
e (c)  y cos x (d)  y cos ecx
dx dx
sin 6 x
 cos8 x dx 
3 1/ 3
4.  d2y   dy 
12. Order and degree of 1   2 
 2  is
 dx   dx 
tan 7 x sec 7 x
(a) c (b) c (a) 2,3 (b) 2,9 (c) 2,6 (d) 2,2
7 7 13. If i+pj+k, 2i+3j+qk are like parallel vectors then
tan 7 x sec 7 x (p,q)=
(c) c (d) c
7 7  3 3 3 3 
k
1  (a)  2,  (b) (2,2) (c)  ,  (d)  ,2 

 dx   2 2 2 2 
5. 1  x2 6 then upper limit k= 14. The angle made by the vector 2i-3j+6k with X-
1/ 3
1 axis is
(a) 3 (b) (c) 1 (d) 2 + 3 (a) Cos 1 ( 2 / 7) (b) Cos 1 (3 / 7)
3
6. The sum of the roots of a equation is 2 and (c) Cos 1 (6 / 7) (d)   Cos 1 (3/ 7)
sum of their cubes is 98, then the equation is-
15. If  is the angle between the vectors 3i+2j+k
(a) x2 + 2x + 15 = 0
and 2i-3j, then the value of  is
(b) x2 + 15 x + 2 = 0
(a) 45 0 (b) 60 0 (c) 90 0 (d) 120 0
(c) 2x2 – 2x + 15 = 0
16. Angle between the planes 2x-y+2z =3,
(d) x2 – 2x – 15 = 0 3x+6y+2z=4 is

3
7. x cos xdx =
(a) Cos
41
(b) Cos
4
1

 21 441
(a)  (b)  2 (c) -  3 (d) 0 (c) Sin
1 4
(d) Sin
1 4

21 441
8. The area of the region bounded by the curve 17. If the distance between the points (k,2) and
y  x 3 , x-axis and the ordinates x=1, x=4 is (3,4) is 8 then k =
255 225 (a) 3  60 (b) 60 (c) - 60 (d) 57
(a) sq. units (b) sq. units 18. The point which is equidistant from the points
4 2
(a, 0, 0), (0, b, 0), (0, 0, c) and (0, 0, 0) is
125 124
(c)
3
sq. units (d)
3
sq. units (a) a , b, c  (b)  a, b, c 
a b c
(c) 2a ,2b,2c  (d)  2 , 2 , 2 
 

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 OURS ACADEMY
19. A coin is tossed two times, then the probability of 31. Which of the following is not true, if A and B are
getting atleast one times head. two matrices each of order n x n, then
(a) 3/4 (b) 1/4 (c) 1/2 (d) 2/3. (a) ( A  B )'  B ' A' (b) ( A  B )'  A' B '
20. The mean of 10 numbers is 25. if 3 is added to (c) ( AB )'  A' B ' (d) ( ABC )'  C ' B ' A'
every number, then a new mean is
(a) 22 (b) 55 (c) 28 (d) none of these.  3 4 
32. If 5A =  4 x  and A AT = AT A=I then x=
21. sin[2 Sin-1 (3/5)] =  
(a) 24/25 (b) 12/25 (c) 48/25 (d) 6/25 (a) 3 (b) -3 (c) 2 (d) -2
 33. If A=( 1 2 3 4) and AB = (3 4 -1)then the order of
22. If Sin-1 x - Cos-1 x = then x = matrix B is
6
(a) 2×3 (b) 3×3 (c) 4×3 (d) 1×3
3 3
(a) 1/2 (b) (c) - 1/2 (d) -  1  2 
2 2  
34. If A    2 1  then minor of a is
8 5 31
23. If Cos-1 ( ) - Cos-1 ( ) = cos-1x then x 2 1  
17 13  
140 220 7 221 (a) -1 (b) 0 (c) 1 (d) -1
(a) (b) (c) (d)
221 221 11 220 a b c
24. If Cos-1 x + Cos-1 y + Cos-1 z =  then b c a
(a) x2 + y2 + z2 = 2xyz 35. =
(b) x2 + y2 + z2 + 2xyz = 0 c a b
(c) x2 + y2 + z2 + 2xyz = 1 (a) a3 + b3 + c3 (b) a3 + b3 + c3 - 3abc
(d) xy + yz + zx = xyz (c) 3abc - a - b - c
3 3 3
(d) 0
  1  1  36. The number of solutions of the equations of 2x
25. co s  co s  1     sin  1     
  7   7  + 5y = 11, 6x + 15y = 1 are ...
(a) 1 (b) 2 (c) 4 (d) 0
1 1 4 37. The equations
(a)  (b) 0 (c) (d)
3 3 9 2 x  4 y  z  0, x  2 y  2 z  5,3x  6 y  7 z  2 have
26. (Adj AT) = (a) unique solution
(a) (Adj A)T (c) Adj A (b) no solution
(c) A T
(d) Adj[A]1 (c) infinite number of solutions
(d) two solutions
27. A 3x3 is a non - singular matrix  A2 (Adj A) =
2 1 i 1 i 1
(a) A A (b) I (c) A I (d) A I
1 i i 1 i
 x  3 2 y  x 0  7 
38. is a
28. If  z  1 4a  z   3 2a , (x+y+z+a) = i 1 i 1 i
   
(a) -1 (b) 0 (c) 1 (d) 8 (a) real number (b) irrational number
(c) complex member (d) Purely imaginary
 1 2   3 3 
29. If A-2B =  3 0
 and 2A-3B =  1 1 then B = cos   Sin 0 
  
 Sin Cos 0 
 -5 7  -5 7   -5 7   -5 -7 
39. Let F(  )=  
(a)  5  (b)   (c)   (d)  
 1  -5 -1  5 -1   -5 -1   0 0 1 
2 3 4
where   R then, [F (  )]-1 is equal to
If A  4 5 6 (a) F(-  ) (b) F(  -1)
30. then 3A =
7 8 9  (c) F(2  ) (d) 0
 6 9 12  6 9 12 40. The value of K so that the system of equations
  4 5 6  x  ky  3 z  0, 3 x  ky  2 z  0,
(a) 12 15 18  (b) 
21 24 27 7 8 9  2 x  3 y  4 z  0 have non-zero solutions then
2 3 4  2 3 4 (a) 33/2 (b) -33/2
12 15 18  4 5 6  (c) 0 (d) 4
(c)   (d) 
 7 8  9 12 24 27

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 OURS ACADEMY

 2 x  3  x 1  53. If y = xx + 2x then
dy
=
41. L im dx
x 1 2 x2  x  3 (a) xx.log(ex)+2x (b) xx + 2x log2
1 1 2 2 (c) xx.log(ex)+2x.log2 (d) xx - 2x log2
(a) (b)  (c) (d) 
10 10 5 5 dy 
54. If x=acos3t, y=asin3t then at t= is
x If x2 dx 3
 1
f  x  x  5 If 2  x  3 L im f  x   1
42. (a) 3 (b) (c)  3 (d)
x  7 If x3
x 3  3 3

(a) -2 (b) -4 (c) 0 (d) 1 55.
d
dx

sin 2 x  3 = 
sin 2  x  5  tan  x  5  cos 2 x  3  cos 2 x  3
L im  (a) (b)
43. x 5
x 2
 25   x  5  2x  3 2 2x  3
(a) 1 (b) 1/10 (b) 0 (d)-6 (c) 2 x  3 cos 2 x  3 (d) cos 2 x  3

Lim
1  3  5  .....  ( 2n  1) x a a
44. = x a
n 
2  4  6  ....  2n 56. If
1  b x a
and  2  then
(a) 0 (b) 1 (c) -1 (d) 5 b b x b x
x  log x
Lim d d
45. x  x  log x
=
(a) 1    2 (b) 1   3 2
(a) 1 (b) -1 (c) 0 (d) 2 dx dx
f  x  f 1 d
(c) 1   2 2 (d) 0
If f  x   x  x  1, then Lx
im 
2
46. dx
1 x 1 dy
(a) 3 (b) 0 (c) -1 (d) 2 57. If cosy=x.cos(a+y) then =
dx
1 cos 2 (a  y ) cos 2 (a  y )
47. The function defined by f (x)  x.sin (a) (b)
x sin a cos a
for x  0 ; =0 for x=0 is ............ at x = 0 cos a cos(a  y )
(a) continuous (b) right continuous (c) 2 (d)
sin ( a  y ) sin a
(c) left continuous (d) can not be determined
dy
sin 2 ax 58. If x=a(cost+log(tan t 2 )), y=asint then =
48. If the function f(x) = 2 for x  0, 1 for x=0 dx
x (a) sin t (b) cot t (c) tan t (d) tan2 t
is continuous at x = 0 then a = dy
1 1 59. If xy = yx then =
(a) ±1 (c) 
(b) 0 (d)  dx
2 3  y ( y  x log y ) y ( y  x log y )
49. The value of f(0) for the function f(x) = (a) x( y log x  x) (b) x( y log x  x)
e x  e x
so that it is continuous everywhere is  x( y log x  x) x( y log x  x)
x (c) y ( y  x log y ) (d) y ( y  x log y )
(a) 1 (b) 1/2 (c) 2 (d) 0
2 x 2  4 f '( x) d  1 2 x 1  x 2 
50. If f '(2) =2, f '' (2)=1 then L im  60. sin  sec 1 =
x 2 x2 dx  1 x2 1  x 2 
(a) 4 (b) 0 (c) 2 (d)  1 2 4 1
51. tan20º + 2 tan50º = (a) 2 (b) 2 (c) 2 (d)
1 x 1 x 1 x 1 x2
(a) tan 70º (b) cot 70º (c) sin 70º (d) tan 30º 61. The set of values of ‘x’ for which f(x) = cos x -
d  1 x  x is decreasing in
52. sin =
dx  a (a) (-  , 0) (b) (0,  ) (c) (-  ,  ) (d) 
1 1
(a) (b) 62.    is increasing in
2 2
a x a  x2
2

1 1 (a) (-5, 0) (b) (0, 5)

(c)
a2  x2
(d)
x2  a2 (c)   ,  5  5,   (d) (-5, 5)

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 OURS ACADEMY

63. The point ont he curve y  3x 2  2x  5 at which e x  e x

the tangent is perpendicular to the line 72.  e x  e  x dx 
x  2y  3  0 (a) log | e x  e  x |  c (b) log | e x  e  x |  c
(a) (0, –5) (b) (0, 5) (c) (–5, 0) (d) (5, 0)
1 x 1 x
(c) log | e  e |  c (d) log | e  e |  c
x x
64. The angle between the curves y = x 3 and
2 2
y  e3(x 1) at (1, 1) is
 x.e
x2
   73. dx =
(a) 0 (b) (c) (d) 1 x2
6 4 2 e c
65. The maximum value of (a) e x 2  c (b)
2
sin(+ /6) + cos( + /6) is attained at
   
(c)  e x  c
2
(d) e x   c
2 2

(a) (b) (c) (d) ex

12 6 3 2 74.  x
(1  2 x) dx =
 cos x dx 
0
66. ex
 9a) xe +c (b) +c
x

(a) sin x0 + c (b) cos x 0  c x

180 (c) 2ex x +c (d) ex x + c
180
sin x  c
0
(d) 180 sin x  c 0
(c)
 Cot x dx 
4
 75.
  3  1
(a)  Cot x  Cot x  x  c
3
67.  1  Sin 2 xdx if x   ,
2 4


3
1
(a) Sin x-Cos x + c (b) Sinx + Cos x + c (b) Cot 3 x  Cot x  c
3
( Sin x  Cos x) 2 1
(c) Cos x-Sin x + c (d) c (c)  Cot x  Cot x  x  c
3

2 3
Sin10 x 1
(d)  Cot x  Cot x  c
3
68.  Cos12 x dx  3

2
tan11 x tan 10 x
 cos
5
(a) c (b) c 76. x. sin 2 xdx =
11 10 0
tan 9 x (a) 2/7 (b) 1/7 (c) -1/7 (d) 3/7
(c) 10 tan9x + c. (d) c a
10 1
1  tan x 77. a dx =
 1  tan x dx   x2
2
69. 0
(a)  /2 (b)  /3 (c)  /4 (d)  /4a
(a) log | 1  tan x |  c 
(b) log | 1  tan x |  c Tanx
78.  Secx  Cosx dx =
(c) log | sin x  cos x |  c 0

(d) log | sin x  cos x |  c (a)  (b)  2 (c) -  (d) 2 

ax
70.  1  a 2 x dx = 79. If cos + cos = 0 = sin + sin, then
cos2 + cos2 is equal to -
(a) –2sin ( + ) (b) –2cos ( + )
(a)
1
log a
 
sin 1 a x  c (b)
1
log a
sin h a x  c   (c) 2sin ( + ) (d) 2cos ( + )

  a   c
5
(c) sin 1 a x  c (d) log a sin 1 x
 x(5  x)
10
80 dx =
| x | dx 
3
71. 0

 x4 x| x |3 512 510
(a) +c (b) +c (a) (b)
4 4 132 132
x4 x3 132 .512
(c) +c (d) c (c) 132.512 (d)
4 3 3

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 OURS ACADEMY
3 d 2 y  dy 
3
dx     3 y  x 2 is
81.  ( x  1)(3  x) = 92. Degree of
dx 2  dx 
1
(a) 4 (b) 2 (c) 3 (d) 1
(a)  (b) -  (c)  2 (d) 0
93. The D.E whose solution is y 2  3ay  x 3 is
2

82.  (| x |  | x  1 |) dx =
0
(a) x 3
 y2 
dy
dx
 3x 2 y (b) x 3
 y2 
dy
dx
 3 xy

(a) 1 (b) -1 (c) 2 (d) 3 dy dy

3
(c) x 3
 y
dx
 3 xy 2 (d) y 2
 x3 
dx
 3 xy
4
dy
83.  | cos x | dx = 94. The solution of
dx
 tan y is

4 (a) log sin x  2 x  c (b) log sin y  x  c
(a) 2 - 2 (b) 2 2 (c) 2 -1 (d) 2  1 (c) log sin y  2 x  c (d) log sin x  2 y  c
2 dx
6 95. I.F of y log y  x  log y is
84.  cos xdx = dy
 2 1
4 5  2 (a) log  log y  (b)
log y
(a) (b) (c) 15  (d) 1
5 4 4
(c) log y
 1  
(d) log log y

85.  1  x 2 dx  dy
96.  e x  y , x  1  y  1 then
(a) 0 (b) 1 (c) 2 (d) 3 dx
86. The area of the curve x  a cos3 t , x  1  y 
y  b sin 3 t in sq. units is 1
(a) 1 (b) e (c) 1 (d) e 
3 ab 3 ab  ab  ab e
(a) (b) (c) (d) 97. The differential equation of all straight lines in a
4 8 4 8
87. The area bounded by the parabola y  4 x and 2
plane passing through  0,1 is
its latusrectum is
(a) y  1  mx (b) y  m  x  1
8 3
(a) sq. units (b) sq. units
3 8 (c) y  xy1 (d) y  xy1  1
1 98. If a,  a are collinear and are in the same direction
(c) 12 sq. units (d) sq. units
3 then  is
88. The area bounded by the ellipse 3 x 2  2 y 2  6 (a) =0 (b) >0
with the co-ordinate axes in sq. units is (c) <0 (d) cannot be determined
 
(a) 6 (b) 8 (c) 12 (d) 3 99. Let A = 2iˆ + 3jˆ + 4k, ˆ AB = 5iˆ + 7jˆ + 6kˆ .

89. The area bounded by the parabola x  4  y 2 Then B =
and the Y-axis, in square units is ˆ ˆ
(a) -(7i+10j+10k) ˆ ˆ ˆ ˆ
(b) (7i-10j+10k)
(a) 3/32 (b) 32/3 (c) 33/2 (d) 16/4
ˆ ˆ ˆ
(c) (7i+10j-10k) ˆ ˆ
(d) (7i+10j+10k)ˆ
90. Area of the region bounded by y  x and y=2 is    
(a) 4 sq. units (b) 2 sq. units 100. If a.iˆ = a.(iˆ + ˆj) =a.(iˆ + ˆj + k)
ˆ then a=
1 (a) î (b) ˆj
(c) 1 sq . units (d) sq. units
2
2 (c) k̂ (d) ˆi + ˆj + kˆ
 dy  d2y
91. Order of  3 x  2 y     5 x  0 is
 dx  dx 2
(a) 2 (b) 1 (c) 4 (d) 3

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 
101. If a  iˆ  2 ˆj  kˆ , b  3iˆ  ˆj  2 kˆ then the 112. If the d.rs of two lines are given by the equations
    2l  m  2n  0 and mn  nl  lm  0 then the angle
angle between a  b and a  b is
between the two lines is
1  4  1 4  (a) 60o (b) 30o
(a) cos   (b) cos  
 91   91  (c) 45o (d) 90 o
 2  1   2 113. The d.r's of the line of intersection of the planes
(c) cos 1   (d) cos  91 
 91    x+y+z-1=0 and 2x+3y+4z-7= 0 are
ˆ ˆ ˆ ˆ ˆ ˆ
102. If the vectors 2 i  j  k , i  4 j   k are (a) 1, 2, -3 (b) 2, 1, -3
(c) 4, 2, -6 (d) 1, -2, 1
perpendicular then   114. The Probability distribution of a random variable
(a) 1 (b) 2 (c) -2 (d) 4 X is given by
103.  iˆ ˆj kˆ    ˆj kˆ iˆ    iˆ kˆ ˆj   X= x 0 1 2 3 4
      P(X = x) 0.4 0.3 0.1 0.1 0.1
(a) 1 (b) -1 (c) 2 (d) -3 The variance of X is
104. The volume of the tetrahedron whose vertices (a) 1. 76 (b) 2.45
are ( 2,1,1) (1,1,2) (0,1,1) and (1,2,1) is (c) 3.2 (d) 4.8
1 2 115. Two unbiased coins whose faces are marked 1
(a) cubic.units (b) cubic.units and 2 are tossed. The mean value of the total of
3 3 the numbers is
4 5 (a) 3 (b) 4 (c) 5 (d) 2
(c) cubic.units (d) cubic.units 116. The probability of getting atleast two heads when
3 3
   an unbiased coin is tossed three times is
105. (a  iˆ)  iˆ  (a  ˆj )  ˆj  (a  kˆ)  kˆ  1 1 1 1
    (a) (b) (c) (d)
(a) 2a (b)  2a (c) a (d)  a 4 3 2 8
106. A point of trisection of the line joining the points 117. If for a B.D. with n=12, the ratio of variance to
(-1, 2), (3,-4) is 1
(a) (1/3, 1) (b) (5/3, -2) mean is , then the probability of 10 successes is
3
(c) (1/3, 2) (d) (5/3, 11) 10 2 10 2
107. The centroid and two vertices of a triangle are 15 2 1 12 2 1
(a) C10     (b) C10    
(4,-8), (-9, 7), (1,4) then the area of the triangle  3  3  3 3
is 10 10
(a) 333 sq.units (b) 166.5 sq.units 2 1
(c)   (d)  
(c) 111 sq.units (d) 55.5 sq.units 3  3
108. Orthocentre of the triangle with vertices (4,1), 118. cos2 48° – sin2 12° =
(7,4), (5,-2) is
(a) (0,0) (b) (1,2) 5 1 5 1
(a) (b)
(c) (3/2, 3/2) (d) (2,1) 4 8
109. The points (a,b), (-a, -b), (b 3, a 3) are 3 1 3 1
(c) (d)
the vertices of a triangle which is 4 2 2
(a) Isosceles (b) Equilateral
(c) Right angled (d) Scalane 1  2 sin 2
FG   IJ
110. XOZ plane divides the join of (2,3,1) and (6,7,1) in 119. H4 K =
the ratio
(a) 3: 7 (b) 2 : 7 (c) -3 : 7 (d) -2 : 7 (a) cos 2 (b) – cos 2
111. The locus of a point whose distance from (c) sin 2 (d) – sin 2
(1, 2, 3) is equal to its distance from the xy-plane 120. cos 24º + cos 5º + cos 175º + cos 204º + cos
is 300º =
(a) x 2  y 2  z 2  2x  4 y  6z  14  0
3
(a) 1/2 (b) – 1/2 (c) (d) 1
(b) x 2  y 2  2x  14  0 2
(c) x 2  y 2  2 x  4 y  6z  14  0
(d) y 2  4 y  6x  14  0

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NDA MATH TEST-18 (Ans Key)

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

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