Explore topic-wise MCQs in Arithmetic Ability.

This section includes 80 Mcqs, each offering curated multiple-choice questions to sharpen your Arithmetic Ability knowledge and support exam preparation. Choose a topic below to get started.

51.

From the top of a 20 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of it's foot is at 45°, then the height of the tower is (√3=1.732)

A. 45.46 m
B. 45.64 m
C. 54.64 m
D. 54.46 m
Answer» D. 54.46 m
Discussion
52.

From a tower 18 m high the angle of elevation of the top of a tall building is 45° and the angle of depression of the bottom of the same building is 60°. What is the height of the building in metres?_x005F_x000D_

A. 12 + 63
B. 6(3 +3)
C. 18 + 2
D. 6(3 + 32 )
Answer» C. 18 + 2
Discussion
53.

From a point P, the angle of elevation of a tower is such that its tangent is 3/4. On walking 560 metres towards the tower the tangent of the angle of elevation of the tower becomes 4/3. What is the height (in metres) of the tower?

A. 720
B. 960
C. 840
D. 1030
Answer» C. 840
Discussion
54.

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

A. 149 m
B. 156 m
C. 173 m
D. 188 m
Answer» D. 188 m
Discussion
55.

A telegraph post is bent at a point above the ground. Its top just touches the ground at a distance of 8√3 m from its foot and makes an angle of 30° with the horizontal. The height (in metre) of the post is

A. 12
B. 16
C. 18
D. 24
Answer» E.
Discussion
56.

A vertical toy 18 cm long casts a shadow 8 cm long on the ground. At the same time a pole casts a shadow 48 m. long on the ground. Then find the height of the pole ?

A. 1080 cm
B. 180 m
C. 108 m
D. 118 cm
Answer» D. 118 cm
Discussion
57.

A tower is broken at a point P above the ground. The top of the tower makes an angle 60° with the ground at Q. From another point R on the opposite sideof Q angle of elevation of point P is 30°. If QR = 180 m, then what is the total height (in metres) of the tower?_x005F_x000D_

A. 90
B. 45√3
C. 45(√3+1)
D. 45(√3+2)
Answer» E.
Discussion
58.

A tower is 50 meters high.Its shadow is x metres shorter when the sun's altitude is 45° than when it is 30° . The value of x in metres is

A. 50√3
B. 50 (√3 -­ 1)
C. 50 (√3 + 1)
D. 50
Answer» C. 50 (√3 + 1)
Discussion
59.

A ladder is resting against a vertical wall and its bottom is 2.5 m away from the wall. If it slips 0.8 m down the wall, then its bottom will move away from the wall by 1.4 m. What is the length of the ladder?

A. 6.2 m
B. 6.5 m
C. 6.8 m
D. 7.5 m
Answer» C. 6.8 m
Discussion
60.

A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60º. What is the distance between the base of the tower and the point P?

A. Data inadequate
B. 8 units
C. 12 units
D. None of these
Answer» B. 8 units
Discussion
61.

A man standing on the bank of river observes that the angle subtended by a tree on the opposite bank is 60°. When he retires 36 m from the bank, he finds that the angle is 30°. The breadth of the river is

A. 15 m
B. 18 m
C. 16 m
D. 11 m
Answer» C. 16 m
Discussion
62.

A Navy captain going away from a lighthouse at the speed of 4[(√3) – 1] m/s. He observes that it takes him 1 minute to change the angle of elevation of the top of the lighthouse from 60 to 45 deg. What is the height (in metres) of the lighthouse?

A. 240√3
B. 480[(√3) – 1]
C. 360√3
D. 280√2
Answer» B. 480[(√3) – 1]
Discussion
63.

A pilot in an aeroplane at an altitude of 200 m 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. (200 + 200/√3) m
B. (200 - 200/√3) m
C. 400 √3 m
D. (400/√3) m
Answer» C. 400 √3 m
Discussion
64.

A ladder 13 m long reaches a window which is 12 m above the ground on side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to each a window 5m high, then the width of the street is :

A. 17 m
B. 16 m
C. 14 m
D. 15 m
Answer» B. 16 m
Discussion
65.

A kite is flying at a height of 50m. If the length of string is 100 m then the inclination of string to the horizontal ground in degree measures is

A. 90
B. 45
C. 60
D. 30
Answer» E.
Discussion
66.

A kite is flying in the sky. The length of string between a point on the ground and kite is 420 m. The angle of elevation of string with the ground is 30 deg. Assuming that there is no slack in the string, then what is the height (in metres) of the kite?

A. 210
B. 140√3
C. 210√3
D. 150
Answer» B. 140√3
Discussion
67.

A helicopter, at an altitude of 1500 m, 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 metres is

A. 1000√3
B. 1000/√3
C. 500√3
D. 500/√3
Answer» B. 1000/√3
Discussion
68.

A flagstaff 17.5 m high casts a shadow of length 40.25 m. What will be the height of a building, which casts a shadow of length 28.75 m under similar conditions ?

A. 14 cm
B. 13.5 cm
C. 12.5 cm
D. 11.4 cm
Answer» D. 11.4 cm
Discussion
69.

A boat is moving away from an observation tower. It makes an angle of depression of 60° with an observer's eye when at a distance of 50m from the tower. After 8 sec., the angle of depression becomes 30°. By assuming that it is running in still water, the approximate speed of the boat is

A. 33 km/hr
B. 42 km/hr
C. 45 km/hr
D. 50 km/hr
Answer» D. 50 km/hr
Discussion
70.

A balloon leaves from a point P rises at a uniform speed. After 6 minutes, an observer situated at a distance of 450√3 metres from point P observes that angle of elevation of the balloon is 60 deg. Assume that point of observation and point P are on the same level. What is the speed (in m/s) of the balloon?

A. 4.25
B. 3.75
C. 4.5
D. 3.45
Answer» C. 4.5
Discussion
71.

A balloon is connected to a meteorological station by a cable of length 130 m, inclined at 60 deg to the horizontal. Find the height of the balloon from the ground. Assume that there is no slack in cable.

A. 110.32 m
B. 173 m
C. 163.28 m
D. 112.58 m
Answer» E.
Discussion
72.

A 25m long ladder is rested on a wall. The foot of the ladder is 7m away from the wall. If the end of the ladder (resting on the wall) slides down 4m, then how far will its foot move away?

A. 5 m
B. 8 m
C. 9 m
D. 10 m
Answer» C. 9 m
Discussion
73.

129 meter from the foot of a cliff on level of ground, the angle of elevation of the top of a cliff is 30°. The height of this cliff is

A. 50√3 metre
B. 45√3 metre
C. 43√3 metre
D. 47√3 metre
Answer» D. 47√3 metre
Discussion
74.

The angle of elevation of the sun, when the length of the shadow of a tree ‚à ö3 times the height of the tree, is:~!

A. 30º
B. 45º
C. 60º
D. 90º
Answer» B. 45¬¨‚à´
Discussion
75.

The angle of elevation of the sun, when the length of the shadow of a tree ‚à ö3 times the height of the tree, is:~!

A. 30º
B. 45º
C. 60º
D. 90º
Answer» B. 45¬¨‚à´
Discussion
76.

From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 100 m high, the distance of point P from the foot of the tower is:$

A. 149 m
B. 156 m
C. 173 m
D. 200 m
Answer» D. 200 m
Discussion
77.

An observer 1.6 m tall is 20‚à ö3 away from a tower. The angle of elevation from his eye to the top of the tower is 30¬∫. The heights of the tower is:$

A. 21.6 m
B. 23.2 m
C. 24.72 m
D. None of these
Answer» B. 23.2 m
Discussion
78.

The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:$

A. 2.3 m
B. 4.6 m
C. 7.8 m
D. 9.2 m
Answer» E.
Discussion
79.

A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60º. What is the distance between the base of the tower and the point P?$

A. 4 ‚à ö3 units
B. 8 units
C. 12 units
D. Data inadequate
E. None of these
Answer» E. None of these
Discussion
80.

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:$

A. 173 m
B. 200 m
C. 273 m
D. 300 m
E. None of these
Answer» D. 300 m
Discussion