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.

551.

If cos + sec =

A. 2
B. 1
C. 0
D. 4
Answer» D. 4
Discussion
552.

The value of (sec

A. 1
B. 2
C. <span style=" text-decoration: overline;">3</span>
D. 0
E. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;"> <span style=" text-decoration: overline;">2</span></td></tr></table>
Answer» D. 0
Discussion
553.

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

A. 8.16
B. 7.32
C. 8.26
D. 8.66
Answer» E.
Discussion
554.

An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 30 and 60 respectively. The distance between the two planes at that instant is

A. 6520 m
B. 6000 m
C. 5000 m
D. 6250 m
Answer» E.
Discussion
555.

If 2 sin + cos = (7 / 3) then the value of (tan sec ) is

A. 0
B. 1
C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></td><td rowspan="2"></td></tr><td align="center">7</td></table>
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>7</center></td><td rowspan="2"></td></tr><td align="center">3</td></table>
Answer» C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></td><td rowspan="2"></td></tr><td align="center">7</td></table>
Discussion
556.

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

A. 173.2 metres
B. 346.4 metres
C. 519.6 metres
D. 692.8 metres
Answer» B. 346.4 metres
Discussion
557.

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

A. 1
B. 2
C. 3
D. 0
Answer» E.
Discussion
558.

If sin 31 = x The value of sec 31 sin 59 isy

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>x<sup>2</sup></center></td></tr><tr><td style="text-align: center;">y <span style=" text-decoration: overline;">y - x </span></td></tr></table>
B. <table><tr><td rowspan="2">-</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>x<sup>2</sup></center></td></tr><tr><td style="text-align: center;">y <span style=" text-decoration: overline;">y - x </span></td></tr></table>
C. <table><tr><td rowspan="2">-</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>y<sup>2</sup></center></td></tr><tr><td style="text-align: center;"> <span style=" text-decoration: overline;">y - x </span></td></tr></table>
D. <table><tr><td rowspan="2">-</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>x<sup>2</sup></center></td></tr><tr><td style="text-align: center;"> <span style=" text-decoration: overline;">y - x </span></td></tr></table>
Answer» B. <table><tr><td rowspan="2">-</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>x<sup>2</sup></center></td></tr><tr><td style="text-align: center;">y <span style=" text-decoration: overline;">y - x </span></td></tr></table>
Discussion
559.

The value of sin 65 + sin 25 + cos 35 + cos 55 is

A. 0
B. 1
C. 2
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center">2</td></table>
E.
Answer» D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center">2</td></table>
Discussion
560.

If the height of a pole is 2

A. 90
B. 45
C. 30
D. 60
Answer» E.
Discussion
561.

Ifsin + cos =5, the value of tan + 1issin - cos 4tan - 1

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>25</center></td></tr><td align="center">16</td></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>41</center></td></tr><td align="center">9</td></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>41</center></td></tr><td align="center">40</td></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>40</center></td></tr><td align="center">41</td></table>
Answer» D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>40</center></td></tr><td align="center">41</td></table>
Discussion
562.

The value of x which satisfies the equation 2 cosec 30 + x sin 60 (3 / 4) tan 30 = 10 is

A. 2
B. 3
C. 0
D. 1
Answer» C. 0
Discussion
563.

The distance between two pillars is 120 metres. The height of one pillar is thrice the other. The angles of elevation of their tops from the mid point of the line connecting their feet are complementary to each other. The height (in metres) of the taller pillar is (Use :

A. 34.64
B. 51.96
C. 69.28
D. 103.92
Answer» E.
Discussion
564.

From two points, lying on the same horizontal line, the angles of elevation of the top of the pillar are and ( < ). If the height of the pillar is h m and the two points lie on the same sides of the piller, then the distance between the two points is

A. h (tan tan ) metre
B. h (cot cot ) metre
C. h (cot cot ) metre
D. <table><tr><td rowspan="2">h</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>tan tan </center></td><td rowspan="2">metre</td></tr><td align="center">tan tan </td></table>
Answer» D. <table><tr><td rowspan="2">h</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>tan tan </center></td><td rowspan="2">metre</td></tr><td align="center">tan tan </td></table>
Discussion
565.

The top of a broken tree touches the ground at a distance of 15 metre from its base. If the tree is broken at a height of 8 metre from the ground, then the actual height of the tree is

A. 17 metre
B. 20 metre
C. 25 metre
D. 30 metre
Answer» D. 30 metre
Discussion
566.

A man standing on the bank of a river observes that the angle of elevation of the top of a tree just on the opposite bank is 60 . But angle of elevation is 30 from a point which is at a distance 20

A. 60 ft
B. 45 ft
C. 30 ft
D. 15 ft
Answer» D. 15 ft
Discussion
567.

The length of shadow of a tower is

A. 45
B. 30
C. 60
D. None
Answer» C. 60
Discussion
568.

Two persons are on either side of a temple, 75 m high, observe the angle of elevation of the top of the temple to be 30 and 60 respectively. The distance between the persons is :

A. 173.2 metre
B. 100 metre
C. 157.7 metre
D. 273.2 metre
Answer» B. 100 metre
Discussion
569.

If the angle of elevation of a cloud from a point 200m above a lake is 30 and the angle of depression of its reflection in the lake is 60 . Then the height of the cloud above the lake is :

A. 100 m
B. 200 m
C. 300 m
D. 400 m
Answer» E.
Discussion
570.

From the top of a 20 metre high building, the angle of elevation of the top of a tower is 60 and the angle of depression of its foot is at 45 , then the height of the tower is (

A. 45.46 metre
B. 45.64 metre
C. 54.64 metre
D. 54.46 metre
Answer» D. 54.46 metre
Discussion
571.

A 1.6 m tall observer is 45 metres away from a tower. The angle of elevation from his eye to the top of the tower is 30 , then the height of the tower in metres is (Take

A. 25.98
B. 26.58
C. 27.58
D. 27.98
Answer» D. 27.98
Discussion
572.

If the length of the shadow of a vertical pole be

A. 60
B. 45
C. 30
D. 90
Answer» D. 90
Discussion
573.

The angle of elevation of the top of a tower from two horizontal points (in opposite sides) at distances of 25 metre and 64 metre from the base of tower are x and 90 x respectively. The height of the tower will be

A. 39 metre
B. 89 metre
C. 1.6 metre
D. 40 metre
Answer» E.
Discussion
574.

If tan (5x 10 ) = cot (5y + 20 ), the value of (x + y) is

A. 15
B. 16
C. 24
D. 20
Answer» C. 24
Discussion
575.

If x sin 60 tan 30 tan 45 = cosec 60 cot 30 sec 45 , then x =

A. 2
B. - 2
C. 6
D. - 4
Answer» B. - 2
Discussion
576.

Which one of the following is true for 0 < q < 90 ?

A. cos cos
B. cos > coscos
C. cos < coscos
D. cos coscos
Answer» C. cos < coscos
Discussion
577.

If sec cos = (3 / 2) where is a positive acute angle, then the value of sec is

A. <table><tr><td rowspan="2">-</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center">2</td></table>
B. 1
C. 2
D. 0
Answer» D. 0
Discussion
578.

If 0 90 and 4 cos 4

A. 30
B. 45
C. 90
D. 60
Answer» B. 45
Discussion
579.

If sin + cosec = 2, the value of sin

A. 1
B. 2
C. 3
D. 4
Answer» C. 3
Discussion
580.

From two points on the ground and lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distances of the two points from the foot of the pillar are 12 metres and 27 metres and the two points lie on the same side of the pillar, then the height (in metres) of the pillar is

A. 12
B. 18
C. 15
D. 16
Answer» C. 15
Discussion
581.

If = 60 , then (1 / 2)

A. <table><tr><td rowspan="2">cot</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2"></td></tr><td align="center">2</td></table>
B. <table><tr><td rowspan="2">sec</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2"></td></tr><td align="center">2</td></table>
C. <table><tr><td rowspan="2">sin</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2"></td></tr><td align="center">2</td></table>
D. <table><tr><td rowspan="2">cos</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2"></td></tr><td align="center">2</td></table>
E.
Answer» E.
Discussion
582.

A pole stands vertically, inside a scalene triangular park ABC. If the angle of elevation of the top of the pole from each corner of the park is same, then in ABC, the foot of the pole is at the

A. centroid
B. circumcentre
C. incentre
D. orthocentre
Answer» C. incentre
Discussion
583.

If2 tan 30 +sec 45 sec 0 = x sec 60 , then the value of x is1 - tan 30

A. 2
B. 1
C. 0
D. - 1
Answer» C. 0
Discussion
584.

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

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center">3</td></table>
B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td><td rowspan="2"></td></tr><td align="center">3</td></table>
C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center">9</td></table>
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td><td rowspan="2"></td></tr><td align="center">9</td></table>
E.
Answer» B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td><td rowspan="2"></td></tr><td align="center">3</td></table>
Discussion
585.

The value of sin 30 cos 45 + 5tan 30 + (3 / 2) sin 90 3 cos 90 is

A. <table><tr><td rowspan="2">3</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>7</center></td><td rowspan="2"></td></tr><td align="center">24</td></table>
B. <table><tr><td rowspan="2">3</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></td><td rowspan="2"></td></tr><td align="center">24</td></table>
C. <table><tr><td rowspan="2">3</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center">24</td></table>
D. <table><tr><td rowspan="2">3</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>5</center></td><td rowspan="2"></td></tr><td align="center">24</td></table>
E.
Answer» B. <table><tr><td rowspan="2">3</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></td><td rowspan="2"></td></tr><td align="center">24</td></table>
Discussion
586.

If 7 sin = 24 cos ; 0 < < ( / 2) , then the value of 14 tan 75 cos 7 sec is equal to

A. 3
B. 4
C. 1
D. 2
Answer» E.
Discussion
587.

Ifcos = a andsin = b, then the value of sin in terms of a and b iscos sin

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>a + 1</center></td><td rowspan="2"></td></tr><td align="center">a - b </td></table>
B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>a - b </center></td><td rowspan="2"></td></tr><td align="center">a + b </td></table>
C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>a - 1</center></td><td rowspan="2"></td></tr><td align="center">a - b </td></table>
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>a - 1</center></td><td rowspan="2"></td></tr><td align="center">a + b </td></table>
Answer» D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>a - 1</center></td><td rowspan="2"></td></tr><td align="center">a + b </td></table>
Discussion
588.

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

A. 2
B. 0
C. 1
D. - 1
Answer» D. - 1
Discussion
589.

If a cos + b sin = p and a sin b cos = q, then the relation between a, b, p and q is

A. a b = p q
B. a + b = p + q
C. a + b = p + q
D. a b = p q
Answer» C. a + b = p + q
Discussion
590.

The angle of elevation of the top of a vertical tower situated perpendicularly on a plane is observed as 60 from a point P on the same plane. From another point Q, 10 m vertically above the point P, the angle of depression of the foot of the tower is 30 . The height of the tower is

A. 15 m
B. 30 m
C. 20 m
D. 25 m
Answer» C. 20 m
Discussion
591.

From two points on the ground lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distance of the two points from the foot of the pillar are 9 metres and 16 metres and the two points lie on the same side of the pillar, then the height of the pillar is

A. 5 m
B. 10 m
C. 7 m
D. 12 m
Answer» E.
Discussion
592.

There are two vertical posts, one on each side of a road, just opposite to each other. One post is108 metre high. From the top of this post, the angle of depression of the top and foot of the other post are 30 and 60 respectively. The height of the other post (in metre) is

A. 36
B. 72
C. 108
D. 110
Answer» C. 108
Discussion
593.

If x = a cos + b sin and y = b cos a sin , then x + y is equal to

A. ab
B. a + b
C. a b
D. 1
Answer» C. a b
Discussion
594.

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 /

A. 75
B. 30
C. 45
D. 60
Answer» C. 45
Discussion
595.

The value of cot 30 - cot 75 is equal totan 15 - tan 60

A. - 1
B. 0
C. 1
D. 2
Answer» B. 0
Discussion
596.

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

A. 300 m/sec
B. 200 m/sec
C. 100 m/sec
D. 150 m/sec
Answer» C. 100 m/sec
Discussion
597.

A man 6 ft tall casts a shadow 4 ft long, at the same time when a flag pole casts a shadow 50 ft long. The height of the flag pole is

A. 80 ft
B. 75 ft
C. 60 ft
D. 70 ft
Answer» C. 60 ft
Discussion
598.

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

A. 1
B. 2
C. 3
D. 4
Answer» C. 3
Discussion
599.

A tower standing on a horizontal plane subtends a certain angle at a point 160 m apart from the foot of the tower. On advancing 100 m towards it, the tower is found to subtend an angle twice as before. The height of the tower is

A. 80 m
B. 100 m
C. 160 m
D. 200 m
Answer» B. 100 m
Discussion
600.

A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40 m long on the ground. The height of the tower is

A. 72 m
B. 60 m
C. 65 m
D. 70 m
Answer» C. 65 m
Discussion