APTITUDE QUIZ
- The angle of elevation of an aeroplane from a point on the ground is 45°. After flying for 15 seconds, the elevation changes to 30°. If the aeroplane is flying at a height of 2500 metres, then the speed of the aeroplane in km/hr is
(a) 600
(b) 600(3+1)
(c) 6003
(d) 600(3+1)
- At a point on a horizontal line through the base of a monument the angle of elevation of the top of the monument is found to be such that its tangent is 15 . On walking 138 metres towards the monument the secant of the angle of elevation is found to be 19312 . The height of the monument (in metre) is
(a) 42
(b) 49
(c) 35
(d) 56
- Two poles of equal height are standing opposite to each other on either side of a road which is 100m wide. From a point between them on road, angle of elevation of their tops are 30° and 60°. The height of each pole (in meter) is
(a) 253
(b) 203
(c) 283
(d) 2033 m
- The angle of elevation of the top of a chimney and roof of the building from a point on the ground are x and 45° respectively. The height of building is h metre. Then the height of the chimney (in metre) is
(a) h cot x + h
(b) h cot x – h
(c) h tan x – h
(d) h tan x + h
- The angle of elevation of the top of a tower from two points A and B lying on the horizontal through the foot of the tower are 15° and 30° respectively. If A and B are on the same side of the tower and AB=48 meter, then the height of the tower is
(a) 253 meter
(b) 24 meter
(c) 242 meter
(d) 96 meter
- Two posts are x metres apart horizontally and the height of one is double that of the other. If from the mid-point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height (in metres) of the shorter post is
(a) x22
(b) x4
(c) x2
(d) x2
- An aeroplane when flying at a height of 5000m from the ground passes vertically above another aeroplane at an instant, when the angles of elevation of the two aeroplanes from the same point on the ground are 60° and 45° respectively. The vertical distance between the aeroplanes at that instant is
(a) 5000 (3 -1) m
(b) 5000 (3-3) m
(c) 5000 (1-13)
(d) 4500 m
- A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° . The man walks some distance towards the tower and then his angle of elevation of the top of the tower is 60° . If the height of tower is 30m, then the distance he moves is
(a) 22 m
(b) 22 3 m
(c) 20 m
(d) 20 3 m
- An aeroplane when flying at a height of 3125m 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 an 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
- A vertical post 15 ft. high is broken at a certain height and its upper part, not completely separated meets the ground at an angle of 30°. Find the height at which the post is broken
(a) 10ft
(b) 5ft
(c) 153 (2-3)ft
(d) 5 3 ft
- 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 15003 m, find the speed of the plane.
(a) 300 m/sec
(b) 200 m/sec
(c) 100 m/sec
(d) 150 m/sec
- There are two temples, one on each bank of a river just opposite to each other. One temple is 54m high. From the top of this temple, the angles of depression of the top and the foot the other temple are 30° and 60° respectively. The length of the other temple is:
(a) 18 m
(b) 36 m
(c) 36 3 m
(d) 18 3 m
- The angle of elevation of the top of a tower from the point P and Q at distance of ‘a’ and ‘b’ respectively from the base of the tower and in the same straight line with it are complementary. The height of the tower is
(a) ab
(b) ab
(c) ab
(d) a2b
- The length of the shadow of a vertical tower on level ground increases by 10 meters when the altitude of the sun changes from 45° to 30°. Then the height of tower is
(a) 53 metre
(b) 10 (3+1) metre
(c) 5 (3+1)metre
(d) 103 metre
.
- 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) 400 33
(b) 16623
(c) 13313
(d) 2003
- From a tower 125 metres high the angle of depression of two objects, which are in horizontal line through the base of the tower are 45° and 30° and they are on the same side of the tower. The distance (in metres) between the object is
(a) 1253
(b) 125(3 -1)
(c) 125 / (3 -1)
(d) 125(3 +1)
- A pilot is 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+ 2003) m
(b) (200- 2003) m
(c) 400 3 m
(d) ( 4003) m
- A telegraph post is bent at a point above the ground. Its top just touches the ground at a distance of 83 m from its feet and makes and angle of 30° with the horizontal. The height (in metre) of the post is
(a) 12
(b) 16
(c) 18
(d) 24
- Two men are on opposite sides of a tower. They measure the angles of elevation of the top of the tower as 30° and 45° respectively. If the height of the tower is 50m, the distance between the two men is (Take 3 =1.73)
(a) 136.6 m/136.6 मी.
(b) 50 3 m/50 3 मी.
(c) 100 3 m/100 3 मी.
(d) 135.5 m/135.5 मी.
- The angles of elevation of top and bottom of flag kept on a flag post from 30 metres distance are 45° and 30° respectively. Height of the flag is (Taking 3 = 1.732)
(a) 12 3 m
(b) 15 m
(c) 14.32 m
(d) 12.68 m
ANSWERS
- d
- a
- a
- c
- b
- a
- c
- d
- d
- b
- b
- b
- a
- c
- c
- b
- a
- d
- a
- d
