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.

101.

If tan =
3
and is acute, then cosec
4
A.
B. 2
C.
Answer» C.
Discussion
102.

If x, y are acute angles, 0 < x + y < 90 and sin (2x 20 ) = cos (2y + 20 ), then the value of tan (x + y) is :

A.
B.
C.
D. 1
Answer» E.
Discussion
103.

If tan = n tan and sin = m sin , then cos is

A.
B.
Answer» D.
Discussion
104.

If tan = 1 + 2 tan ( , are positive acute angles), then 2 cos cos is equal to

A. 0
B.
C. 1
D. - 1
Answer» B.
Discussion
105.

If be acute angle and cos = (15 / 17) , then the value of cot
(90 ) is

A.
Answer» C.
Discussion
106.

If 2 (cos sin ) = 1 ( is a positive acute angle), then cot is equal to

A. -
B.
C.
D. 1
E.
Answer» E.
Discussion
107.

If sin sec (30 + ) = 1 (0 < a < 60 ), then the value of sin + cos 2 is

A. 1
B. 0
C.
D.
Answer» B. 0
Discussion
108.

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

A. 0
B. 1
Answer» D.
Discussion
109.

If be a positive acute angle satisfying cos + cos4 = 1, then the value of tan + tan4 is

A.
B. 1
C. 0
Answer» C. 0
Discussion
110.

If
sin + cos
= 3, then the value of sin4 cos4 is
sin - cos

A.
B.
C.
Answer» D.
Discussion
111.

If 2cos sin = (1 / 2) , (0 < q < 90 ) the value of 2 sin + cos is

A.
B.
Answer» D.
Discussion
112.

If sin cos = (7 / 13) and 0 < < 90 , then the value of sin + cos is

A.
B.
Answer» B.
Discussion
113.

If be acute and tan + cot = 2, then the value of tan5 + cot10 is

A. 1
B. 2
C. 3
D. 4
Answer» C. 3
Discussion
114.

If sin + cosec = 2, then the value of sin5 +cosec5 when 0 90 , is

A. 0
B. 1
C. 10
D. 2
Answer» E.
Discussion
115.

If A = sin + cos4 , for any value of , then the value of A is

A. 1 A 2
B.
C.
Answer» C.
Discussion
116.

A person of height 6ft. wants to pluck a fruit which is on a (26 / 3) ft. high tree. If the person is standing (8 / 3) ft. away from the base of the tree, then at what angle should he throw a stone so that it hits the fruit?

A. 75
B. 30
C. 45
D. 60
Answer» C. 45
Discussion
117.

The two banks of a canal are straight and parallel. A, B, C are three persons of whom A stands on one bank and B and C on the opposite banks. B finds the angle ABC is 30 , while C finds that the angle ACB 60 . If B and C are 100 metres apart, the breadth of the canal is

A. 20
B. metres
C. 25
D. metres
Answer» D. metres
Discussion
118.

The base of a triangle is 12 3 cm and two angles at the base are 30 and 60 respectively. The altitude of the triangle is

A. 12 cm
B. 6 cm
C. 10
D. cm
E. 9 cm
Answer» E. 9 cm
Discussion
119.

From the top of a hill 200 m high, the angle of depression of the top and the bottom of a tower are observed to be 30 and 60 . The height of the tower is (in m) :

A.
B.
C. 200
Answer» D.
Discussion
120.

From an aeroplane just over a straight road, the angles of depression of two consecutive kilometre stones situated at opposite sides of the aeroplane were found to be 60 and 30 respectively. The height (in km) of the aeroplane from the road at that instant was (Given 3 = 1.732)

A. 0.433
B. 8.66
C. 4.33
D. 0.866
Answer» E.
Discussion
121.

From an aeroplane just over a straight road, the angles of depression of two consecutive kilometre stones situated at opposite sides of the aeroplane were found to be 60 and 30 respectively. The height (in km) of the aeroplane from the road at that instant, is

A.
B.
Answer» D.
Discussion
122.

If cos + sec = 2, the value of cos6 + sec6 is

A. 4
B. 8
C. 1
D. 2
Answer» E.
Discussion
123.

From an aeroplane just over a river, the angle of depression of two palm trees on the opposite bank of the river are found to be 60 and 30 respectively. If the breadth of the river is 400 metres, then the height of the aeroplane above the river at that instant is (Assume 3 = 1.732)

A. 173.2 metres
B. 346.4 metres
C. 519.6 metres
D. 692.8 metres
Answer» B. 346.4 metres
Discussion
124.

The angle of depression of a point situated at a distance of 70 m from the base of a tower is 60 . The height of the tower is :

A. 35
B. m
C. 70
D. m
E. 70 m
Answer» C. 70
Discussion
125.

A pilot in an aeroplane at an altitude of 200 metre observes two points lying on either side of a river. If the angles of depression of the two points be 45 and 60 , then the width of the river is

A. 400
B. metre
Answer» B. metre
Discussion
126.

If sin + cosec = 2, then value of sin100 + cosec100 is equal to :

A. 1
B. 2
C. 3
D. 100
Answer» C. 3
Discussion
127.

If cos + cos = 2, then the value of tan&3 + sin5 is :

A. - 1
B. 0
C. 1
Answer» C. 1
Discussion
128.

If 5 tan = 4, then
5sin - 3cos
is equal to
5sin - 2cos

A.
B.
Answer» D.
Discussion
129.

If x sin 45 = y cosec 30 , then
x4
is equal to
y4
A. 4
B. 6
C.
D. 2
E. 8
Answer» B. 6
Discussion
130.

If cosec cot =
7
, the value of cosec is :
2
A.
B.
Answer» D.
Discussion
131.

If sec + tan = &radic3 (0 90 ), then tan 3 is

A. undefined
B.
C. 3
Answer» B.
Discussion
132.

The angle of elevation of a tower from a distance of 100 metre from its foot is 30 . Then the height of the tower is

A. 50
B. metre
C. 100
D. metre
E.
Answer» E.
Discussion
133.

A 10 metre long ladder is placed against a wall. It is inclined at an angle of 30 to the ground. The distance (in m) of the foot of the ladder from the wall is (Given 3 = 1.732)

A. 8.16
B. 7.32
C. 8.26
D. 8.66
Answer» E.
Discussion
134.

If the height of a pole is 2 3 metre and the length of its shadow is 2 metre, then the angle of elevation of the sun is

A. 90
B. 45
C. 30
D. 60
Answer» E.
Discussion
135.

If is an acute angle and sin ( + 18 ) = (1 / 2) , then the value of in circular measure is :

A.
B.
Answer» C.
Discussion
136.

From a point 20 m away from the foot of a tower, the angle of elevation of the top of the tower is 30 . The height of the tower is

A. 10
B. m
C. 20
D. m
E.
Answer» E.
Discussion
137.

The angle of elevation of the top of a tower of height 100 3 metre from a point at a distance of 100 metre from the foot of the tower on a horizontal plane is

A. 45
B. 60
C. 30
Answer» C. 30
Discussion
138.

The angle of elevation of the top of a tower from a point on the ground is 30 and moving 70 metres towards the tower it becomes 60 . The height of the tower is

A. 10 metre
B. 10
C. metre
D. 35
E. metre
Answer» E. metre
Discussion
139.

If a pole of 12 m height casts a shadow of 4 3 m long on the ground, then the sun s angle of elevation at that instant is

A. 30
B. 60
C. 45
D. 90 16 cm is
Answer» C. 45
Discussion
140.

If tan4 + tan2 = 1 then the value of cos4 + cos2 is

A. 2
B. 0
C. 1
D. 1
Answer» D. 1
Discussion
141.

The value of 8 (sin6 + cos6 ) 12 (sin4 + cos4 ) is equal to

A. 20
B. 20
C. 4
D. 4
Answer» D. 4
Discussion
142.

The value of cos2 20 + cos2 70 is :

A.
B. 2
C. 1
Answer» E.
Discussion
143.

x, y be two acute angles, x + y < 90 and sin(2x 20 ) = cos (2y + 20 ), the value of tan (x + y) is

A.
B. 1
C. 2 +
Answer» D.
Discussion
144.

If r sin = 3 r cos = 1, rhen values of r and are : (0 90 )

A. r = 1, = 30
B. r = 1/2, = 30
C. r =
D. , = 30
E. r = 2, = 60
Answer» E. r = 2, = 60
Discussion
145.

If 2 tan2 = 6 and 0 < < 45 , then the value of sin + 3cos 2tan2 is

A. 2
Answer» C.
Discussion
146.

If sin + sin = 1 then cos + cos4 is equal to

A. None
B. 1
C.
Answer» C.
Discussion
147.

The numerical value of
cos 45
+
cos 60
-
tan 30
-
sin 30
is
sin 60 sin 45 cot 45 cot 30

A.
B.
C.
D.
Answer» C.
Discussion
148.

The value of tan80 tan10 + sin2 70 + sin270 + sin220 is

A. 0
B. 1
C. 2
Answer» D.
Discussion
149.

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

A. 1
B. 0
C.
Answer» D.
Discussion
150.

The value of (sec245 cot245 ) (sin230 + sin260 ) is

A. 1
B. 2
C. 0
Answer» D.
Discussion