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JEE Main Math Previous Year Papers Heights and Distances Questions Answer Keys Solutions

Welcome to AMBiPi (Read as: एम्बीपाई) (Amans Maths Blogs). JEE Mains and JEE Advanced exams are the engineering entrance exams for taking admission in IITs, NITs and other engineering colleges. In this article, you will get JEE Main Math Previous Year Paper Height and Distance Questions Answer Keys Solutions.

JEE Mains Mathematics Height and Distance Questions Bank

JEE Height and Distance Questions No:1

The upper (3/4) th portion of a vertical pole subtends an angle tan-1 (3/5) at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is

[2003]

Option A: 80 m

Option B: 20 m

Option C: 40 m

Option D: 60 m

Option C: 40 m

JEE Height and Distance Questions No:2

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 meters away from the tree the angle of elevation becomes 30° The breadth of the river is

[2004]

Option A: 60 m

Option B: 30 m

Option C: 40 m

Option D: 20 m

Option D: 20 m

JEE Mathematics Height and Distance Questions No:3

A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (= a) subtends an angle of 60° at the foot of the tower, and the angle of elevation of the top of the tower from A and B is 30°. The height of the tower is

[2007]

Option A: a / √3

Option B: a √3

Option C: 2a / √3

Option D: 2a√3

Option A: a / √3

JEE Main Math Height and Distance Questions No:4

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°. He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is 45°. Then the height of the pole is

[2008]

Option A: (7√3 / 2) (1/√3 – 1) m

Option B: (7√3 / 2) (√3 + 1) m

Option C: (7√3 / 2) (√3 – 1) m

Option D: (7√3 / 2) (1/√3 + 1) m

Option B: (7√3 / 2) (√3 + 1) m

Height and Distance JEE Questions No:5

The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be α. After moving a distance 2 metres from P towards the foot of the tower, the angle of elevation changes to β. Then the height (in metres) of the tower is

[2014]

Option A: 2 sinα sinβ / sin (α – β)

Option B: sinα sinβ / cos (β – α)

Option C: 2 sin (β – α) / sinα sinβ

Option D:  cos (β – α) / sinα sinβ

Option A: 2 sinα sinβ / sin (α β)

Height and Distance JEE Main Questions No: 6

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45°. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30°. Then the speed (in m/s) of the bird is

[2014]

Option A: 20√2

Option B: 20 (√3 – 1)

Option C: 40 (√2 – 1)

Option D: N40 (√3 – √2)

Option B: 20 (√3 – 1)

Height and Distance Questions for JEE Mains Questions No: 7

Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation at a point O on this line and all the poles are on the same side of O. If the height of the longest pole is ‘h’ and the distance of the foot of the smallest pole from O is ‘a’; then the distance between two consecutive poles, is

[2015]

Option A: h cosα – a sinα / 9 sinα

Option B: h sinα + a cosα / 9 sinα

Option C: h cosα – a sinα / 9 cosα

Option D: h sinα – a cosα / 9 cosα

Option A: h cosα – a sinα / 9 sinα

Height and Distance Questions and Answers No:8

If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the tower, are 30°, 45° and 60° respectively, then the ratio, AB: BC, is:

[2015]

Option A: 1:√3

Option B: 2:3

Option C: √3:1

Option D: √3:√2

Option C: √3:1

Height and Distance Questions with Solutions No:9

The angle of elevation of the top of a vertical tower from a point A, due cast of it is 45° The angle of elevation of the top of the same tower from a point B, due south of A is 30°.If the distance between A and B is 54√2 m, then the height of the tower (in metres), is

[2016]

Option A: 108

Option B: 36√3

Option C: 54√3

Option D: 54

Option D: 54

JEE Mains Height and Distance Questions No: 10

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30°. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60°. Then the time taken (in minutes) by him, from B to reach the pillar, is

[2016]

Option A: 20

Option B: 5

Option C:  6

Option D: 10

Option B: 5

JEE Mains Math Height and Distance Questions No:11

Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB. If ∠BPC = β, then tan β is equal to

[2002]

Option A: 4/9

Option B: 6/7

Option C: 1/4

Option D: 2/9

Option D: 2/9

Height and Distance Questions for JEE Questions No: 12

A tower T1, of height 60 m is located exactly opposite to a tower T2 of height 80 m on a straight road. From the top of T1, if the angle of depression of the foot of T2 is twice the angle of elevation of the top of T2, then the width (in m) of the road between the feet of the towers T1, and T2

[2018]

Option A: 20√2

Option B: 10√2

Option C: 10√3

Option D: 20√3

Option D: 20 3

Height and Distance Problems for Class 11 Questions No: 13

An aeroplane flying at a constant speed, parallel to the horizontal ground, √3km above it, is observed at an elevation of 60° from a point on the ground. If, after five seconds, its elevation from the same point, is 30°, then the speed (in km/hr) of the aeroplane is

[2018]

Option A: 1500

Option B: 750

Option C: 720

Option D: 1440

Option D: 1440

Height and Distance Problems for Class 12 Questions No: 14

A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road If it takes 18 min, for the angle of depression of the car to change from 30° to 45°, then after this, the time taken (in min) by the car to reach the foot of the tower, is

[2018]

Option A: 9 (1 + 3)

Option B: (9/2) (√3 – 1)

Option C: 18 (1 + √3)

Option D: 18 (√3 – 1)

Option A: 9 (1 + 3)

Height and Distance Problems for Class 11 JEE Questions No: 15

PQR is a triangular park with PQ = PR = 200 m. AT.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively 45°, 30° and 30°, then the height of the tower (in m) is

[2018]

Option A: 50

Option B: 100 √3

Option C: 50 √2

Option D: 100

Option D: 100

Height and Distance Problems for Class 12 JEE Questions No: 16

Consider a triangular plot ABC with sides AB = 7 m BC 5 m and CA=6 m. A vertical lamp-post at the mid point D of AC subtends an angle 30° at B. The height (in m) of the lamp-post is

[2019]

Option A: (3/2) 21

Option B: (2/3) 21

Option C: 2 21

Option D: 7 3

Option B: (2/3) 21

JEE Height and Distance Questions No:17

ABC is a triangular park with AB = AC = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at A and B are cot-1 (3√2) and cosec-1 (2√2) respectively, then the height of the tower (in metres) is

[2019]

Option A: 100 / 3√3

Option B: 10 √5

Option C: 20

Option D: 25

Option C: 20

JEE Height and Distance Questions No:18

The angle of elevation of a cloud C from a point P, 200 m above a still lake is 30°. If the angle of depression of the image of C in the lake from the point P is 60°, then PC (in m) is equal to:

[2020]

Option A: 100

Option B: 200√3

Option C: 400

Option D: 400√3

Option C: 400

JEE Mathematics Height and Distance Questions No:19

Two vertical poles AB = 15 m and CD = 10 m are standing apart on a horizontal ground with points A and C on the ground. If P is the point of intersection of BC and AD, then the height of P (in m) above the line AC is

[2020]

Option A: 20 / 3

Option B:  5

Option C: 10 / 3

Option D: 6

Option D: 6

JEE Main Math Height and Distance Questions No:20

The angle of elevation of the summit of a mountain from a point on the ground is 45°. After climbing up on km to wards the summit at an inclination of 30° from the ground, the angle of elevation of the summit is found to be 60°. Then the height (in km) of the summit from the ground is

[2020]

Option A: 3 – 1 / √3 + 1

Option B: 3 + 1 / √3 – 1

Option C: 1 / √3 – 1

Option D: 1 / √3 + 1

Option C: 1 / 3 – 1

Height and Distance JEE Questions No:21

The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45°. After walking a distance of 80 meters towards the top, up a slope inclined at an angle of 30° to the horizontal plane, the angle of elevation of the top of the hill becomes 75°. Then the height of the hill (in meters) is

[2020]

Correct Ans : 80

Height and Distance JEE Main Questions No: 22

A ray of light coming from the point (2, 2√3) is incident at an angle 30° on the line x = 1 at the point A. The ray gets reflected on the line x = 1 and meets x-axis at the point B. Then, the line AB passes through the point

[2020]

Option A: (3, -1/√3)

Option B: (4, –√3/2)

Option C: (3, –√3)

Option D: (4, –√3)

Option C: (3, – 3)

Height and Distance Questions for JEE Mains Questions No: 23

The angle of elevation of a jet plane from a point A on the ground is 60°. After a flight of 20 seconds at the speed 432 km/hour, the angle of elevation changes to 30°. If the jet plane is flying at a constant height, then its height is

[2021]

Option A: 1800√3 m

Option B: 3600 √3 m

Option C: 2400 √3 m

Option D: 1200 √3 m

Option D: 1200 3 m

Height and Distance Questions and Answers No:24

Two vertical poles are 150 m apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an observer finds the angles of elevation of their tops to be complementary, then the height of the shorter pole (in meters) is

[2021]

Option A: 20√3

Option B: 25√3

Option C: 30

Option D: 25

Option B:  25 3

Height and Distance Questions with Solutions No:25

A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A, with uniform speed. At the point, angle of depression of the boat with the man’s eye is 30° (Ignore man’s height). After sailing for 20 seconds, towards the base of the tower (which is at the level of water), the boat has reached a point B, where the angle of depression is 45°. Then the time taken (in seconds) by the boat from B to reach the base of the tower is

[2021]

Option A: 10√3

Option B: 10

Option C: 10 (√3 + 1)

Option D: 10 (√3 – 1)

Option C:  10 (3 + 1)

JEE Mains Height and Distance Questions No: 26

A spherical gas balloon of radius 16 meter subtends an angle 60° at the eye of the observer A while the angle of elevation of its center from the eye of A is 75°. Then the height (in meter) of the top most point of the balloon from the level of the observer’s eye is

[2021]

Option A: 8 (2 + 2√3 + √2)

Option B: 8 (√6 + √2 + √2)

Option C: 8 (√2 + 2 + √3)

Option D: 8 (√6 – √2 + 2)

Option B: 8 (√6 + √2 + √2)

JEE Mains Math Height and Distance Questions No:27

A vertical pole fixed to the horizontal ground is divided in the ratio 3 : 7 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground 18 m away from the base of the pole, then the height of the pole (in meters) is

[2021]

Option A: 12√15

Option B: 12√10

Option C: 8√10

Option D: 6√10