JEE Questions for Maths Trigonometric Ldentities And Equations Quiz 21

The circum-radius of the triangle whose sides are 13, 12 and 5 is

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15
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13/2
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15/2
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6

Maths-Trigonometric ldentities and Equations-58087.png

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0%
2)
0%
0%

The area of the equilateral triangle which contains three coins of unity radius is
Maths-Trigonometric ldentities and Equations-58093.png

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0%
2)
0%
0%

For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is

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2)
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0%

The angle of elevation of the top of a tower at a point on the ground is 30^o. If on walking 20 metres toward the tower, the angle of elevation become 60^o, then the height of the tower is

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10 metres
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2)
0%
0%
None of these

The angle of elevation of tower at a point distant d metres from it base is 30^o. If the tower is 20 metres high, then the value of d is

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0%
2)
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0%

The angle of elevation of the top of the tower observed from each of the three points A, B, C on the ground, forming a triangle is the angle α. If R is the circum radius of the triangle ABC, then the height of the tower is

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0%
2)
0%
0%

The angle of elevation of the top of a tower from a point A due south of the tower is α and from a point B due east of the tower is β. If AB = d, then the height of the tower is

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0%
2)
0%
0%

A person standing on the bank of a river observes that the angle subtend by a tree on the opposite bank is 60^o. When he retires 40 metres from the bank, he finds the angle to be 30^o. The breadth of the river is

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20 m
0%
40 m
0%
30 m
0%
60 m

A vertical pole consists of two parts, the lower part being one third of the whole. At a point in the horizontal plane through the base of the pole and distance 20 metres from it, the upper part of the pole subtends an angle whose tangent is 1/2. The possible heights of the pole are

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20 m and 20√3 m
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20 m and 60 m
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16 and 48 m
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None of these

Maths-Trigonometric ldentities and Equations-58124.png

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0%
2)
0%
0%

An observer on the top of a tree, finds the angle of depression of a car moving the tree to be 30^o. After 3 minutes this angle becomes 60^o. After how much more time, the car will reach the tree

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4 min
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4.5 min
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1.5 min
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2 min

A house of height 100 metres subtends a right angle at the windows of an opposite house. If the height of the window be 64 metre, then the distance between the two houses is

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48m
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36m
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54m
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72m

The length of the shadow of a pole inclines at 10^o to the vertical towards the sun is 2.05 metres, when the elevation of the sun is 38^o. The length of the pole is

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0%
2)
0%
0%
None of these

AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60^o. He moves away from the pole along the line BC to a point D such that CD = 7cm. From D the angle of elevation of the point A is 45^o. Then the height of the pole is

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0%
2)
0%
0%

The horizontal distance between two towers is 60 metres and the angular depression of the top of the first tower as seen from the top of the second, is 30^o. If the height of the second tower be 150 metres, then the height of the first tower is

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0%
2)
0%
0%
None of these

From the top of a light house 60 meters height with its base at the sea level, the angle of depression of a boat is 15^o. The distance of the boat from the foot of light house is

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0%
2)
0%
0%
None of these

An observer in a boat finds that the angle of elevation of a tower standing on the top of a cliff is 60^o and that of the top is cliff is 30^o. If the height of the tower be 60 metres, then the height of the cliff is

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30 m
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60√3 m
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20√3 m
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None of these

A tower subtends an angle α at a point A in the plane of its base and the angle of depression of the foot of the tower at a point l metres just above A is β. The height of the tower is

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0%
2)
0%
0%

The angle of elevation of a tower from s point A due south of it is 30^o and from a point B due west of it is 45^o. If the height of the tower be 100 m, then AB =

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150 m
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200 m
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173.2 m
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141.4 m

A aeroplane flying horizontal 1 km above the ground is observed at an elevation of 60^o and after 10 seconds the elevation is observed to be 30^o. The uniform speed of the aeroplane is km/h is

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240
0%
240√3
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60√3
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None of these

From a point a metre above a lake the angle of elevation of a cloud is α and the angle of depression of its reflection is β. The height of the cloud is

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0%
2)
0%
0%
None of these

ABCD is a rectangular field. A vertical lamp post of height 12 m stand at the corner A. If the angle of elevation of its top from B is 60^o and from C is 45^o, then the area of the field is

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0%
2)
0%
0%

The shadow of a tower is found to be 60 metre shorter when the sun’s altitude changes from 30^o to 60^o. The height of the tower from the ground is approximately equal to

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62 m
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301 m
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101 m
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52 m

At a distance 2h from the foot of a tower of height h, the tower and a pole at the top of the tower subtend equal angles. Height of the pole should be

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0%
2)
0%
0%

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 be 6 metres, then the height of the first of the first house is

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0%
2)
0%
0%
None of these

The angle of elevation of the sun, when the shadow of the pole is √3 times the height of the pole is

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60o
0%
30o
0%
45o
0%
15o

A ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle 60^o with the horizontal and height of the house he 6√3 metres, 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
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None of these

If the angles of elevation of two from the middle point of the line joining their feet be 60^o and 30^o respectively, then the ration of their heights is

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2:1
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1: √2
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3:1
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1: √3

At a point on the ground the angle of elevation of a tower is such that its cotangent is 3/5. On walking 32 metres towards the tower the cotangent of the angle of elevation is 2/5. The height of the tower is

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160 m
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120 m
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64 m
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None of these

A ladder rests against a wall making an angle α with the horizontal. The foot of the ladder is pulled away from the wall through a distance x, so that it slides a distance y down the wall making an angle β with the horizontal. The correct relation is

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0%
2)
0%
0%

The base of a cliff is circular. From the extremities of a diameter of the base the angles of elevation of the top of the cliff are 30^o and 60^o. If the height of the cliff be 500 metres, then the diameter of the base of the cliff is

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0%
2)
0%
0%

The angle of elevation of the top of a tower from the top of a house is 60^o and the angle of depression of the base is 30^o. If the horizontal distance between the house and the tower be 12 m, then the height of the tower is

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0%
2)
0%
0%

A man whose eye is 1.5 metres above the ground observes the angle of elevation of a tower to be 60^o. If the distance of the man from the tower be 10 metres, the height of the tower is

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0%
2)
0%
0%
None of these

A tower subtend an angle of 30^o at a point distant d from the foot of the tower and on the same levels a the foot of the tower. At a second point h vertically above the first, the depression of the foot of the tower is 60^o. The height of the tower is

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0%
2)
0%
0%

A tower of height b subtends an angle at a point O on the level of the foot of the tower and at a distance a from the foot of the tower. If a pole mounted on the tower also subtends an equal angle at O, the height of the pole is

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0%
2)
0%
0%

A tree is broken by wind, its upper part touches the ground at a point 10 metres from the foot of the tree and makes an angle of 45^o with the ground. The total length of tree is

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15 metres
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20 metres
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0%

The angle of depression of a ship from the top of a tower 30 metre high is 60^o, then the distance of ship from the base of tower is

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30 m
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2)
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0%
10 m

The angle of elevation of a stationary sound form a point 2500 m above a lake is 15^o and the angle of depression of its reflection in the lake is 45^o. The eight of cloud above the lake level is

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2500√3 m
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2500 m
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500√3 m
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None of these

From an aeroplane vertically over a straight horizontally road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be α and β, then the height in miles of aeroplane above the road is

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0%
2)
0%
0%

A balloon is observed simultaneously from three points A, B and C on a straight road directly under it. The angular elevation at B is twice and at C is thrice that of A, If the distance between A and B is 200 metre and the distance between B and C is 100 metres, then the height of balloon is given by

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50m
0%
50√3 m
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50√2 m
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None of these

Maths-Trigonometric ldentities and Equations-58222.png

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100 ft
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120 ft
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150 ft
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None of these

A flag-pot 20 m high standing on the top of a house subtends an angle whose tangent is 1/6 at a distance 70 m from the foot of the house. The height of the house is

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30 m
0%
60m
0%
50 m
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None of these

A balloon is coming down at the rate of 4 m/min and its angle of elevation is 45^o from a point on the ground which has been reduced to 30^o after 10 minutes. Balloon will be on the ground at a distance of how many metres from the observer

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0%
2)
0%
0%
None of these

A person standing on the bank of a river finds that the angle of elevation of the top of tower on the opposite bank is 45^o. Then which of the following statement is correct

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Breadth of the river is twice the height of the tower
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Breadth of the river and the height of the tower are the same
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Breadth of the river is half of the height of the tower
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None of the above

AB is a vertical pole resting at the end A on the level ground. P is a point on the level ground such that AP = 3 AB. If C is the mid-point of AB and CB subtends an angle β at P, the value of tanβ is

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0%
2)
0%
0%
None of these

Two straight roads intersect at an angle of 60^o. A bus on one road is 2 km away from the intersection and a car on the other road is 3 km away from the intersection. Then the direct distance between the two vehicles is

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1 km
0%
√2 km
0%
4 km
0%
√7 km

If a flagstaff of 6 metres high placed on the top of a tower throws a shadow of 2√3 metres along the ground, then the angle (in degrees) that the sun makes with the ground is

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60o
0%
80o
0%
75o
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None of these

The angle of elevation of cliff a point A on the ground and a point B, 100 m vertically at A are α and β respectively. The height of the cliff is

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0%
2)
0%
0%

A flag-staff of 5 m high stands on a building of 25 m high. At an observer at a height of 30 m, the flag-staff and the building subtend equal angles. The distance of the observer from the top of the flag-staff is

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0%
2)
0%
0%
None of these

JEE Questions for Maths Trigonometric Ldentities And Equations Quiz 21 - MCQExams.com

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Practice Maths Quiz Questions and Answers

JEE Questions for Maths Trigonometric Ldentities And Equations Quiz 21 - MCQExams.com

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Practice Maths Quiz Questions and Answers

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