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JEE Questions for Maths Heights And Distances Quiz 1 - MCQExams.com
JEE
Maths
Heights And Distances
Quiz 1
A house of height 100 m subtends a right angle at the window of an opposite house. If the height of the window is 64 m, then the distance between the two houses is
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0%
48 m
0%
36 m
0%
54 m
0%
72 m
ABCD is a square plot. The angle of elevation of the top of a pole standing at D from A or C is 30° and that from B is θ, then tan θ is equal to
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0%
√6
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1/√6
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√3/2
0%
√2/2
A vertical pole PO is standing at the centre 0 of a square ABCD. If AC subtends an ∠ 90° at the top P of the pole, then the angle subtended by a side of the square at P is
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30°
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45°
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60°
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None of these
The angles of elevation of the top of a tower at two points, which are at distances a and b from the foot in the same horizontal line and on the same side of the tower, are complementary. The height of the tower is
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ab
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√ab
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√(a/b)
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√(b/a)
Angles of elevation of the top of a tower from three points (collinear) A ,B and C on a road leading to the foot of the tower are 30°, 45° and 60°, respectively. The ratio of AB to BC is
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√3 : 1
0%
√3 : 2
0%
1 : 2
0%
2 : √3
From the top of a cliff 50 m high, the angles of depression of the top and bottom of a tower are observed to be 30° and 45°. The height of tower is
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0%
50 m
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50√3 m
0%
50 (√3 -m
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50 (1 - √3/3 ) m
ABC is a triangular park with ,AB = AC = 100 m. A clock tower is situated at the mid-point of BC. The angle of elevation, if the top of the tower at A and B are cot
-1
3 2 and cosec
-1
2.6, respectively. The height of the tower is
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16 m
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25 m
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50 m
0%
None of these
P is a point on the segment joining the feet of two vertical poles of heights a and b. The angles of elevation of the tops of the poles from P are 45° each. Then, the square of the distance between the tops of the poles is
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0%
(a2+b2)/2
0%
a2 + b2
0%
2(a2 + b2)
0%
4(a2 + b2)
The base of a cliff is circular. From the extremities of a diameter of the base angles of elevation of the top of the cliff are 30° and 60°. If the height of the cliff is 500 m, then the diameter of the base of the cliff is
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2000/√3 m
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1000/√3 m
0%
2000/√2 m
0%
1000√3 m
A round balloon of radius r subtends an angle a at the eye of the observer, while the angle of elevation of its center is β. The height of the centre of balloon is
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0%
0%
2)
0%
0%
The shadow of tower standing on a level ground is
x
meters long when the Sun\'s altitude is 30°, while it is y meters long when the altitude is 60°. If the height of the tower is 45.√3/2 m then
x
- y is equal to
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45 m
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45 √3 m
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45/√3 m
0%
45 . √3/2 m
The angle of elevation of the top of a TV tower from three points A, B and C in a straight line through the foot of the tower are α, 2α and 3α, respectively. If AB = α, then height of the tower is
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a tan α
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a sin α
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a sin 2α
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a sin 3α
A flagpole stands on a building of height 450 ft and an observer on a level ground is 300 ft from the base of the building. The angle of elevation of the bottom of the flagpole is 30° and the height of the flagpole is 50 ft. If 0 is the angle of elevation of the top of the flagpole, then tanθ is
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0%
4/3√3
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√3/2
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9/2
0%
√3/5
0%
(4√3+1)/6
From an aeroplane flying, vertically above a horizontal road, the angles of depression of two consecutive stones on the same side of the aeroplane are observed to be 30° and 60°, respectively. The height (in km) at which the aeroplane is flying, is
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0%
4/√3
0%
√3/2
0%
2/√3
0%
2
A house subtends a right angle at the window of an opposite house and the angle of elevation of the window from the bottom of the first house is 60
o
. If the distance between the two houses is 6 m, then the height of the first house is
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8√3 m
0%
6√3 m
0%
4√3 m
0%
None of these
The angle of elevation of top of a tower from a point on the ground is 30° and it is 60° when it is viewed from a point located 40 m away from the initial point towards the tower. The height of the tower is
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- 20√3 m
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√3/20 m
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- √3/20 m
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20√3 m
A ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle of 60° with the horizontal and height of the house is 6√3 in, then the length of the ladder is
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12√3 m
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12 m
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12/√3 m
0%
None of these
A man from the top of a 100 m high tower sees a car moving towards the tower at an angle of depression of 30°. After sometime, the angle of depression becomes 60°. The distance travelled by the car during this is
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0%
100√3 m
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200√3/3 m
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100√3 /3 m
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200√3 m
From the top of a tower, the angle of depression of a point on the ground is 60°. If the distance of this point from the tower is 1/(√3+m, then the height of the tower is
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0%
(4√3)/2 m
0%
(√3 + 3)/2 m
0%
(3 - √3)/ 2 m
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√3/2 m
0%
√3 + 1m
The angle of elevation of the top of a hill from a point is α. After walking b meters towards the top up a slope inclined at an angle β to the horizon, the angle of elevation of the top becomes γ . Then, the height of the bill is
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0%
0%
2)
0%
0%
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