Explore topic-wise MCQs in Maths.

This section includes 74 Mcqs, each offering curated multiple-choice questions to sharpen your Maths knowledge and support exam preparation. Choose a topic below to get started.

51.

A straight tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 30 with the ground. The distance from the foot of the tree to the point, where the top touches the ground is 10m. Find the total height of the tree

A. 10( 3+1) m
B. 10( 3-1) m
C. 10 3 m
D. $${10 3 over3}m$$
Answer» D. $${10 3 over3}m$$
Discussion
52.

An observer on the top of a mountain, 500 m above the sea level, observes the angles of depression of the two boats in his same place vision to be 45 and 30 respectively. Then the distance between the boats, if the boats are on the same side of the mountain, is

A. 366 m
B. 699 m
C. 456 m
D. 584 m
Answer» B. 699 m
Discussion
53.

An Aeroplan flying horizontally at a height of 3 km. Above the ground is observed at a certain point on earth to subtend an angle of 60 . After 15 sec flight, its angle of elevation is changed to 30 . The speed of the Aeroplan (taking 3 = 1.732)

A. 235.93 m/sec.
B. 236.25 m/sec.
C. 230.63 m/sec.
D. 230.93 m/sec.
Answer» E.
Discussion
54.

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 50 m 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. 45 km/h
B. 50 km/h
C. 33 km/h
D. 42 km/h
Answer» B. 50 km/h
Discussion
55.

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. 500 3
B. $${500 over 3}m$$
C. 100 3
D. $${1000 over 3}m$$
Answer» D. $${1000 over 3}m$$
Discussion
56.

The angle of elevation of an aeroplane from a point on the ground is 60 . After flying for 15 second, the angle of elevation changes to 30 . If the Aeroplane is flying at a height of 4500 meter, then what is the speed (in m/s) of aeroplane?
A. $$ {150 sqrt{3}}$$
B. $$ {200 sqrt{3}}$$
C. $$ {100 sqrt{3}}$$
D. $$ {50 sqrt{3}}$$
Answer» C. $$ {100 sqrt{3}}$$
Discussion
57.

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 30o. Assuming that there is no slack in the string, then what is the height (in metres) of the kite?
A. $$ {210 sqrt{3}}$$
B. 240
C. $$ {240 sqrt{3}}$$
D. 210
Answer» E.
Discussion
58.

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 3 = 1.732 )

A. 27.58
B. 27.98
C. 25.98
D. 26.58
Answer» B. 27.98
Discussion
59.

The distance between two pillars is 120 meters. The height of one pillar is thrice of the other pillar. The angles of elevation of their tops from the midpoint of the line connecting their feet are complementary to each other. The height (in metres) of the pillar is (use : 3 = 1.732 )
A. 69.28
B. 103.92
C. 34.64
D. 51.96
Answer» C. 34.64
Discussion
60.

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 side of Q angle of elevation of point P is 30 . If QR = 180 m, then what is the total height (in meters ) of the tower ?

A. 45( 3+1)
B. 45( 3+2)
C. 90
D. 45 3
Answer» C. 90
Discussion
61.

A Navy captain going away from a lighthouse at the speed of 4[(73) -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 . What is the height (in meters) of the lighthouse?

A. 360 3
B. 280 2
C. 240 3
D. 480[( 3)-1]
Answer» D. 480[( 3)-1]
Discussion
62.

The upper part of a tree is broken over by the wind makes an angle of 60 with the ground. The distance between the root and the point where top of the tree touches the ground is 25 metres. What was the height (in metres) of the tree?

A. 98.25
B. 120.24
C. 84.14
D. 93.3
Answer» E.
Discussion
63.

An Aeroplan is flying horizontally at a height of 1.8 km above the ground. The angle of elevation of plane from point X is 60 and after 20 seconds, its angle of elevation from X becomes 30 , If point X is on ground, then what is the speed (in km / hr.) of Aeroplan?

A. 201 3
B. 305 3
C. 216 3
D. 105 3
Answer» D. 105 3
Discussion
64.

The shadow of the tower becomes 60 meters longer when the altitude of the sun changes from 45 to 30 . Then the height of the tower is

A. 30( 3+1) m
B. 30( 3-1) m
C. 20( 3+1) m
D. 24( 3+1) m
Answer» B. 30( 3-1) m
Discussion
65.

The distance between two parallel poles is 40 3 m. The angle of depression of the top of the second pole, when seen from the top of first pole, is 30 . What will be the height of second tower if the first pole is 100m long?

A. 35 3
B. 60 m
C. 50 3 m
D. 80 m
Answer» C. 50 3 m
Discussion
66.

An earthing wire connected to the top of an electricity pole has its other end inside the ground. The foot of the wire is 1.5 m away from the pole and the wire is making an angle of 60 with the level of the ground. Determine the height of pole.

A. 3
B. $${ 3 over2}m$$
C. $${3 3 over2}m$$
D. 3 m
Answer» D. 3 m
Discussion
67.

A ladder is placed along a wall such that its upper end is touching the top of the wall. The foot of the ladder is 10 ft away from the wall and the ladder is making an angle of 60 with the ground. When a man starts climbing on it, it slips and now ladder makes an angle of 30 with ground. How much did the ladder slip?

A. 30 ( 3-1) ft
B. 18 ( 3-1) ft
C. 10 ( 3-1) ft
D. 20 ( 3-1) ft
Answer» D. 20 ( 3-1) ft
Discussion
68.

The shadow of a tower, when the angle of elevation of the sun is 60 is found to be 15 m shorter than when it is 45 . Then height of the tower is

A. 41.5 m
B. 35.5 m
C. 26.5m
D. 20.5m
Answer» C. 26.5m
Discussion
69.

If the angle of elevation of the Sun changes from 30 to 45 , the length of the shadow of a pillar decreases by 20 meters. The height of the pillar is

A. 10 ( 3-1 ) m
B. 1 ( 3 + 1 ) m
C. 20 ( 3-1) m
D. 20 ( 3 + 1) m
Answer» C. 20 ( 3-1) m
Discussion
70.

If the length of a shadow of a pole on a level ground is twice the length of that pole, the angle of elevation of the sun is:-
A. 30
B. 45
C. 60
D. None of these
Answer» E.
Discussion
71.

A kite is flying at a height of 123 meter. The thread attached to it assumed to be stretched straight and makes an angle of 60 with the level ground. The length of the string will be

A. 142 m
B. 140 m
C. 139 m
D. 138 m
Answer» B. 140 m
Discussion
72.

A ladder rests against a wall at a height of 10 meters. If the ladder makes 30 along the ground. Find the distance from the wall of the foot of the ladder.
A. $$ {10 over{ sqrt{3}}}$$
B. $$ {20 sqrt{3}} over{3}$$
C. $$ {10 sqrt{3}}$$
D. $$ {20 sqrt{3}}$$
Answer» D. $$ {20 sqrt{3}}$$
Discussion
73.

The angles of elevation of the top of a temple, from the foot and the top of a building 48 m high, are 60o and 30o respectively. The height of the temple is more than the building. The height of the temple is-
A. 72 m
B. 75 m
C. 60 m
D. 65 m
Answer» B. 75 m
Discussion
74.

An observer who is 1.62-meter-tall is 45 meters away form a pole. The angle of elevation of the top of the pole from his eyes is 30 . The height ( in meter) of the pole is closet to:
A. 26.8
B. 27.6
C. 26.2
D. 25.8
Answer» C. 26.2
Discussion