Explore topic-wise MCQs in Aptitude.

This section includes 639 Mcqs, each offering curated multiple-choice questions to sharpen your Aptitude knowledge and support exam preparation. Choose a topic below to get started.

51.

If is an acute angle and tan + cot = 2, then the value of tan5 + cot5 is

A. 1
B. 2
C. 3
D. 4
Answer» C. 3
Discussion
52.

If sec + tan = 2, then the value of sin is
(assume that 0 < < 90 )

A. 0.4
B. 0.5
C. 0.6
D. 0.8
Answer» D. 0.8
Discussion
53.

In a ABC, B = ( / 3) , C = ( / 4) and D divides BC internally in the ratio 1 : 3 then sin (sin BAD / sin CAD) is equal to

A.
B.
Answer» D.
Discussion
54.

If is a positive acute angle and cosec = 3 , then the value of cot cosec is

A.
B. None of these
Answer» F.
Discussion
55.

If and are positive acute angles, sin (4 ) = 1 and cos (2 + ) = (1 / 2) , then the value of sin ( + 2 ) is

A. 0
B. 1
C.
D.
Answer» E.
Discussion
56.

If cos =
3
 then the value of sin . sec . tan is
5
A.
B.
Answer» C.
Discussion
57.

If = 60 , then (1 / 2) 1 + sin + (1 / 2) 1 - sin is equal to

A.
Answer» E.
Discussion
58.

If x sin 60 .tan 30 = sec 60 .cot 45 , then the value of x is

A. 2
B. 2
C.
D. 4
E. 4
Answer» D. 4
Discussion
59.

If 29 tan = 31, then the value of
1 + 2sin cos
is equal to
1 - 2sin cos

A. 810
B. 900
C. 540
D. 490
Answer» C. 540
Discussion
60.

In ABC, = B 90 and AB : BC = 2 : 1. The value of sin A + cot C is

A. 3 +
B.
C. 2 +
D. 3
Answer» C. 2 +
Discussion
61.

If tan = 2, then the value of
8sin + 5cos
is :
sin3 + 2cos3 + 3 cos

A.
B.
C.
Answer» B.
Discussion
62.

If tan 7 tan 2 = 1, then the value of tan 3 is

A.
B. -
C.
Answer» D.
Discussion
63.

If tan + cot = 2, then the value of tann + cotn (0 < < 90 , n is an integer) is

A. 2
B. 2
C.
D. 2n
E. 2
Answer» B. 2
Discussion
64.

If
sec + tan
=
5
, then sin is equal to
sec - tan 3
A.
B.
Answer» B.
Discussion
65.

If x = a sec cos , y = b sec sin , z = c tan , then the value of
x
+
y
-
z
is :
a b c

A. 1
B. 4
C. 9
D. 0
Answer» B. 4
Discussion
66.

The angles of depression of two ships from the top of a light house are 45 and 30 toward east. If the ships are 200m apart, the height of the light house is (Take 3 =1.73)

A. 273 metre
B. 270 metre
C. 253 metre
D. 263 metre
Answer» B. 270 metre
Discussion
67.

If sec x + cos x = 2, then the value of sec16 x + cos16 x will be

A.
B.
C. 2
D. 1
E. 0
Answer» C. 2
Discussion
68.

If x = a cos cos , y = a cos sin and z = a sin , then the value of (x2 + y2 + z2) is

A. 2a
B. 4a
C. 9a
D. a
Answer» E.
Discussion
69.

If sinA + sin2A = 1, then what is the value of cos2A + cos4A ?

A. 1
B. 2
Answer» B. 2
Discussion
70.

If sin =
3
and 0 < < 90 , then the value of tan ( 15 ) is
2
A. 1
B.
C.
Answer» B.
Discussion
71.

If r sin = 1, r cos = 3 then the value of (r2 tan ) is

A. 4
B. 4
Answer» D.
Discussion
72.

If sin4 + cos4 = 2 sin2 cos2 , is an acute angle, then the value of tan is

A. 1
B. 2
C.
D.
E. 0
Answer» B. 2
Discussion
73.

The value of (1 + tan2 ) (1 sin2 )

A. 2
B. 1
C. 1
D. 2
Answer» C. 1
Discussion
74.

A helicopter, at an altitude of 1500 metre, finds that two ships are sailing towards it, in the same direction. The angles of depression of the ships as observed from the helicopter are 60 and 30 respectively. Distance between the two ships, in metre is

A.
B. 1000
C. 500
D.
Answer» B. 1000
Discussion
75.

At a point on a horizontal line through the base of a monument, the angle of elevation of the top of the monument is found to be such that its tangent is 1/5. On walking 138 metres towards the monument the secant of the angle of elevation is found to be
193
.
12
The height of the monument (in metre) is

A. 35
B. 49
C. 42
D. 56
Answer» D. 56
Discussion
76.

An aeroplane when flying at a height of 5000 m from the ground passes vertically above another aeroplane at an instant, when the angles of elevation of the two aeroplanes from the same point on the ground are 60 and 45 respectively. The vertical distance between the aeroplanes at that instant is

A. 5000 (
B. - 1 ) m
C. 5000 (3 -
D. ) m
E. 4500 m
Answer» D. ) m
Discussion
77.

Two posts are x metres apart and the height of one is double that of the other. If from the mid-point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then the height (in metres) of the shorter post is

A.
B. x
C.
Answer» B. x
Discussion
78.

A telegraph post is bent at a point above the ground due to storm. Its top just meets the ground at a distance of 8 3 metres from its foot and makes an angle of 30 , then the height of the post is :

A. 16 metres
B. 23 metres
C. 24 metres
D. 10 metres
Answer» D. 10 metres
Discussion
79.

Two poles of equal height are standing opposite to each other on either side of a road which is 100 m wide. From a point between them on road, angle of elevation of their tops are 30 and 60 . The height of each pole (in metre) is

A. 25
B. 20
C. 28
D. 30
Answer» B. 20
Discussion
80.

The angle of elevation of a tower from a distance 100 m from its foot is 30 . Height of the tower is :

A.
B. 50
C. m
D. 100
E. m
Answer» B. 50
Discussion
81.

The angle of elevation of the top of a tower from the point P and Q at distance of a and b respectively from the base of the tower and in the same straight line with it are complementary. The height of the tower is

A.
B. ab
C. a
D. b
Answer» B. ab
Discussion
82.

The angle of elevation of an aeroplane from a point on the ground is 60 . After 15 seconds flight, the elevation changes to 30 . If the aeroplane is flying at a height of 1500 3 m, find the speed of the plane

A. 300 m/sec
B. 200 m/sec
C. 100 m/sec
D. 150 m/sec
Answer» C. 100 m/sec
Discussion
83.

The shadow of a tower is 3 times its height. Then the angle of elevation of the top of the tower is

A. 45
B. 30
C. 60
D. 90
Answer» C. 60
Discussion
84.

The angle of elevation of a tower from a distance 50 m from its foot is 30 . The height of the tower is

A. 50
B. m
C. 75
D. m
E.
Answer» C. 75
Discussion
85.

If the angle of elevation of a balloon from two consecutive kilometre-stones along a road are 30 and 60 respectively, then the height of the balloon above the ground will be

A.
B. 3
C. km
Answer» B. 3
Discussion
86.

The maximum value of sin2 + cos2 is

A.
B. 1
C. 2
D. 3
Answer» C. 2
Discussion
87.

The angle of elevation of sun changes from 30 to 45 , the length of the shadow of a pole decreases by 4 metres, the height of the pole is
( Assume 3 = 1.732)

A. 1.464 m
B. 9.464 m
C. 3.648 cm
D. 5.464 m
Answer» E.
Discussion
88.

Find the simplest numerical value of 3 (sin x cos x)4 + 4 (sin6x + cos6x) + 6(sinx + cosx)

A. 12
B. 10
C.
D. 21
E. 13
Answer» E. 13
Discussion
89.

A telegraph post is bent at a point above the ground due to starm. Its top just touches the ground at a distance of 10 3 metre from its foot and makes an angle of 30 with the horizontal. Then height (in metres) of the telegraph post is

A. 30
B. 24
C. 20
D. 25
Answer» B. 24
Discussion
90.

If a 48 m tall building has a shadow of 48 3 m., then the angle of elevation of the sun is

A. 15
B. 60
C. 45
D. 30
Answer» E.
Discussion
91.

If cosec 39 = x, the value of (1 / cosec 51 ) + sin 39 + tan 51 (1 / sin 51 sec 39 is

A.
B.
C. x 1
D. 1 x
Answer» D. 1 x
Discussion
92.

The value of tan1 tan2 tan3 ....... tan89 is :

A. 1
B. 0
C.
D.
Answer» B. 0
Discussion
93.

If tan 15 = 2 3 , the value of tan 15 cot 75 + tan 75 cot 15 is

A. 14
B. 12
C. 10
D. 8
Answer» B. 12
Discussion
94.

If q be an acute angle and 7 sin + 3 cos = 4, then the value of tan is

A.
B.
C.
D. 1
E. 0
Answer» C.
Discussion
95.

The value of cot .tan(90 ) sec(90 ) cosec + (sin 25 + sin2 65 ) + 3 (tan 5 tan 15 . tan 30 . tan75 . tan 85 ) is :

A. 1
B. - 1
C. 2
D. 0
Answer» B. - 1
Discussion
96.

The cliff of a mountain is 180 m high and the angles of depression of two ships on the either side of cliff are 30 and 60 . What is the distance between the two ships?

A. 400 metre
B. 400
C. metre
D. 415.68 metre
E. 398.6 metre
Answer» D. 415.68 metre
Discussion
97.

The value of
cot 30 - cot 75
is :
tan 15 - tan 60

A. 0
B. 1
C.
D. -1
E. - 1
Answer» E. - 1
Discussion
98.

The value of cot 10 . cot 20 . cot 60 . cot 70 . cot 80 is

A. 1
B. -1
C.
D.
E.
Answer» E.
Discussion
99.

Maximum value of (2 sin + 3 cos ) is

A. 2
B.
C.
D.
E. 1
Answer» C.
Discussion
100.

If sin (A B) = (1 / 2) and cos (A + B) = (1 / 2) where A > B > 0 and A + B is an acute angle, then the value B is

A.
B.
C.
Answer» C.
Discussion