HARD

JEE Main

IMPORTANT

Earn 100

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

50% studentsanswered this correctly

Important Questions on Heights and Distances

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Heights and Distances>JEE Main - 4th April 2015>Q 20

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

A B : B C

, is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Heights and Distances>JEE Main - 11th April 2015>Q 21

Let

10

vertical poles standing at equal distances on a straight line, subtend the same angle of elevation

α

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

a

; then the distance between two consecutive poles, is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Heights and Distances>JEE Main - 6th April 2014>Q 22

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

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Heights and Distances>JEE Main - 28 June 2022 Shift 1>Q 23

Let

A B

and

P Q

be two vertical poles,

160 m

apart from each other. Let

C

be the middle point of

B

and

Q

, which are feet of these two poles. Let

\frac{π}{8}

and

θ

be the angles of elevation from

C

P

and

A

, respectively. If the height of pole

P Q

is twice the height of pole

A B

, then

\tan^{2} θ

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Heights and Distances>JEE Main - 29 June 2022 Shift 2>Q 24

From the base of a pole of height

20

meter, the angle of elevation of the top of a tower is

60 °

. The pole subtends an angle

30 °

at the top of the tower. Then the height of the tower is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Heights and Distances>JEE Main - 25 July 2022 Shift 1>Q 25

A tower

P Q

stands on a horizontal ground with base

Q

on the ground. The point

R

divides the tower in two parts such that

Q R = 15 m

. If from a point

A

on the ground the angle of elevation of

R

60 °

and the part

P R

of the tower subtends an angle of

15 °

A

, then the height of the tower is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Heights and Distances>JEE Main - 27 July 2022 Shift 1>Q 26

Let a vertical tower

A B

of height

2 h

stands on a horizontal ground. Let from a point

P

on the ground a man can see upto height

h

of the tower with an angle of elevation

2 α

. When from

P

, he moves a distance

d

in the direction of

\vec{A P}

, he can see the top

B

of the tower with an angle of elevation

α

. If

d = \sqrt{7} h

, then

\tan α

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Heights and Distances>JEE Main - 27 July 2022 Shift 2>Q 27

The angle of elevation of the top

P

of a vertical tower

P Q

of height

10

from a point

A

on the horizontal ground is

45 °

. Let

R

be a point on

A Q

and from a point

B

, vertically above

R

, the angle of elevation of

P

60 °

. If

∠ B A Q = 30 °, A B = d

and the area of the trapezium

P Q R B

α

, then the ordered pair

(d, α)

Important Questions on Heights and Distances

Learn and Prepare for any exam you want !