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.

1.

The angles of elevation of an aeroplane flying vertically above the ground, as observed from the two consecutive stones, 1 km apart; are 45 and 60 aeroplane from the ground is :

A. (
B. + 1) km.
C. (
D. + 3) km.
Answer» E.
Discussion
2.

If the angle of elevation of the top of a pillar from the ground level is raised from 30 to 60 , the length of the shadow of a pillar of height 50 3 will be decreased by

A. 60 metre
B. 75 metre
C. 100 metre
D. 50 metre
Answer» D. 50 metre
Discussion
3.

From a point P on a level ground, the angle of elevation to the top of the tower is 30 . If the tower is 100 metre high, the distance of point P from the foot of the tower is (Take 3 = 1.73)

A. 149 metre
B. 156 metre
C. 173 metre
D. 188 metre
Answer» D. 188 metre
Discussion
4.

Find the angular elevation of the Sun when the shadow of a 15 metre long pole is (15 / 3) metre.

A. 45
B. 60
C. 30
D. 90
Answer» C. 30
Discussion
5.

If A is an acute angle and cot A + cosec A = 3, then the value of sin A is

A. 1
B.
C.
D. 0
Answer» C.
Discussion
6.

If x = a sec and y = b tan then
a
-
b
= ?
x y

A. 1
B. 2
C. 3
D. 4
Answer» B. 2
Discussion
7.

The value of tan 11 tan 17 tan 79 tan 73 is

A.
B. 0
C. 1
D.
Answer» D.
Discussion
8.

If sin + sin = 1, then the value of cos2 + 3 cos10 + 3 cos8 + cos6 1 is

A. 1
B. 2
C. 3
D. 0
Answer» E.
Discussion
9.

If for any acute angle A, sin A + sin A = 1, then the value of cos A + cos4 A is

A. - 1
B. 1
C. 2
D. 0
Answer» C. 2
Discussion
10.

If 0 90 and 4 cos 4 3 cos + 3 = 0 then the value of is

A. 30
B. 45
C. 90
D. 60
Answer» B. 45
Discussion
11.

If sin ( + 30 ) =
3
, then the value of cos is
12
A.
B.
Answer» D.
Discussion
12.

If a sin + b cos = c, then a cos b sin is equal to

A.
B.
C.
D.
E.
Answer» D.
Discussion
13.

If x = a sec , y = b tan , then
x
-
y
is
a b

A. - 1
B. 0
C. 1
D. 2
Answer» D. 2
Discussion
14.

If sin (60 x) = cos (y + 60 ), then the value of sin (x y) is

A.
B.
C. 1
Answer» C. 1
Discussion
15.

If sin (3 ) = 1 and cos (2 + ) = (1 / 2) , then the value of tan is

A. 0
B.
C. 1
D.
E.
Answer» C. 1
Discussion
16.

If cos4 sin4 = (2 / 3) , then the value of 1 2 sin2 is

A.
B. 1
C. 0
Answer» B. 1
Discussion
17.

If cos + sec = 3 , then the value of cos3 + sec3 is

A. 2
B. 1
C. 0
D. 4
Answer» D. 4
Discussion
18.

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

A.
B.
C. 1
Answer» D.
Discussion
19.

If x cos 30 . sin 60 =
tan 45 . sec 60
then the value of x is
cosec 60

A.
B.
C.
Answer» D.
Discussion
20.

If tan (A + B) = AAAA and tan (A B) = (1 / 3) , A + B) < 90 , A B, then A is

A. 90
B. 30
C. 45
D. 60
Answer» D. 60
Discussion
21.

If tan = 2, then the value of
cosec - sec
is
cosec + sec

A.
B.
Answer» C.
Discussion
22.

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

A. 1
B. 3
C.
D. None
Answer» D. None
Discussion
23.

If tan =
3
, then the value of
4sin - 2cos
is equal to
44sin + 3cos

A.
B.
C.
D.
Answer» B.
Discussion
24.

If sec + tan = 2 + 5 , then the value of sin + cos is :

A.
B.
Answer» B.
Discussion
25.

If sin + cosec = 2, then the value of sin9 + cosec9 is :

A. 3
B. 2
C. 4
D. 1
Answer» C. 4
Discussion
26.

If sec + tan = 2, then the value of sec is

A.
B. 5
C.
D.
E.
Answer» D.
Discussion
27.

The value of 3 (sin x cos x)4 + 6 (sin x + cos x)2+ 4 (sin6 x + cos6 x) is

A. 14
B. 11
C. 12
D. 13
Answer» E.
Discussion
28.

If tan + cot = 2, then the value of tan100 + cot100 is

A. 2
B. 0
C. 1
D.
E.
Answer» B. 0
Discussion
29.

From a point on a bridge across the river, the angles of depression of the banks on opposite sides of the river are 30 and 45 respectively. If the bridge is at a height of 2.5 m from the banks, then the width of the river is (Take 3 = 1.732)

A. 5.83 metre
B. 6.83 metre
C. 5.76 metre
D. 6.87 metre
Answer» C. 5.76 metre
Discussion
30.

If cos x + cos x = 1, the numerical value of (sin12x + 3 sin10x + 3 sin8x + sin6x l) is :

A. - 1
B. 2
C. 0
D. 1
Answer» D. 1
Discussion
31.

If (r cos 3 ) + (r sin 1) = 0 then the value of
r tan + sec
is equal to
r sec + tan

A.
B.
C.
D.
Answer» B.
Discussion
32.

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

A.
B.
C.
D. 1
E. 2
Answer» E. 2
Discussion
33.

The greatest value of sin4 + cos4 is

A. 2
B. 3
C. 1
Answer» E.
Discussion
34.

If tan cot = 0, find the value of sin + cos .

A. 0
B. 1
C.
D.
E. 2
Answer» D.
Discussion
35.

The value of
1
-
1
is
(1 + tan )(1 + cot )
A. 1
B.
C.
Answer» C.
Discussion
36.

If cos4 sin4 = (2 / 3) , then the value of 1 2 sin2 is

A.
B. 0
C.
D.
Answer» D.
Discussion
37.

If sin + sin = 1, then the value of cos + cos4 is

A. 2
B. 4
C. 0
D. 1
Answer» E.
Discussion
38.

The simplest value of cot 9 cot 27 cot 63 cot 81 is

A. 0
B. 1
C. - 1
D.
E.
Answer» C. - 1
Discussion
39.

If 7 sin + 3 cos = 4, (0 < < 90 ), then the value of tan is

A.
B.
C. 1
D.
Answer» B.
Discussion
40.

If 0 < < 90 and 2 sec = 3 cosec , then is

A.
B.
Answer» D.
Discussion
41.

If x = a (sin + cos ), y = b (sin cos ) then the value of
x
+
y
is
a b

A. 0
B. 1
C. 2
D. 2
Answer» D. 2
Discussion
42.

If tan = 1 e , then the value of sec + tan3 cosec is

A. (2 + e )
B. (2 - e )
C. (2 + e )
D. (2 - e )
E.
Answer» E.
Discussion
43.

If sec + tan = 5, then the value of tan (tan + 1 / tan - 1) is

A.
B.
C.
Answer» E.
Discussion
44.

If q is a positive acute angle and 4 cos 4 cos + 1 = 0, then the value of tan ( 15 ) is equal to

A. 0
B. 1
C.
D.
Answer» C.
Discussion
45.

If cos sin = (1 / 3) , where 0 q ( / 2) , then the value of cos4 sin4 is

A.
Answer» B.
Discussion
46.

The value of
cos 60 + 4sec 30 - tan 45
is
sin 30 + cos 30

A.
B.
C.
Answer» C.
Discussion
47.

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

A. 2
B. 0
C. 1
D. - 1
Answer» D. - 1
Discussion
48.

If sin =
3
, then the value of
tan + cos
is equal to
5cot + cosec

A.
B.
Answer» C.
Discussion
49.

If tan =
1
and 0 , < <
, then the value of
cosec - sec
is
112cosec + sec

A.
B.
Answer» D.
Discussion
50.

The simple value of tan 1 . tan 2 . tan 3 ....... tan 89 is

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