Height and Distance PYQs - Last 5 Years

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Practice 28 JEE Main Mathematics questions from Height and Distance. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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2019-2023

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Last 5 Years Height and Distance Questions

Showing 28 of 28 filtered questions.

1Height And Distance

From the top \(\mathrm{A}\) of a vertical wall \(\mathrm{AB}\) of height \(30 \mathrm{~m}\), the angles of depression of the top \(\mathrm{P}\) and bottom \(\mathrm{Q}\) of a vertical tower \(\mathrm{PQ}\) are \(15^{\circ}\) and $$60^{\circ...

2Height And Distance

The angle of elevation of the top \(\mathrm{P}\) of a tower from the feet of one person standing due South of the tower is \(45^{\circ}\) and from the feet of another person standing due west of the tower is \(30^{\circ}\). If the height of...

3Height And Distance

From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60\(^\circ\). The pole subtends an angle 30\(^\circ\) at the top of the tower. Then the height of the tower is :

4Height And Distance

The angle of elevation of the top of a tower from a point A due north of it is \(\alpha\) and from a point B at a distance of 9 units due west of A is \(\cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\). If the distance of the point B from the t...

5Height And Distance

Let AB and PQ 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 \({\pi \over 8}\) and \(\theta\) be the angles of elevation from C to P and A, respectively. If ...

6Height And Distance

A horizontal park is in the shape of a triangle \(\mathrm{OAB}\) with \(\mathrm{AB}=16\). A vertical lamp post \(\mathrm{OP}\) is erected at the point \(\mathrm{O}\) such that \(\angle \mathrm{PAO}=\angle \mathrm{PBO}=15^{\circ}\) and $$\an...

7Height And Distance

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 \(2 \alpha\). When from \(P\), he moves a distance $...

8Height And Distance

The angle of elevation of the top P of a vertical tower PQ of height 10 from a point A on the horizontal ground is \(45^{\circ}\). Let R be a point on AQ and from a point B, vertically above \(\mathrm{R}\), the angle of elevation of $$\math...

9Height And Distance

A tower PQ stands on a horizontal ground with base \(Q\) on the ground. The point \(R\) divides the tower in two parts such that \(Q R=15 \mathrm{~m}\). If from a point \(A\) on the ground the angle of elevation of \(R\) is \(60^{\circ}\) a...

10Height And Distance

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, th...

11Height And Distance

Two poles, AB of length a metres and CD of length a + b (b \(\ne\) a) metres are erected at the same horizontal level with bases at B and D. If BD = x and tan\(\angle\)ACB = \({1 \over 2}\), then :

12Height And Distance

A 10 inches long pencil AB with mid point C and a small eraser P are placed on the horizontal top of a table such that PC = \(\sqrt 5\) inches and \(\angle\)PCB = tan-1(2). The acute angle through which the pencil must be rotated about C s...

13Height And Distance

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

14Height And Distance

A man is observing, from the top of a tower, a boat speeding towards the lower from a certain point A, with uniform speed. At that point, angle of depression of the boat with the man's eye is 30\(^\circ\) (Ignore man's height). After sailin...

15Height And Distance

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...

16Height And Distance

The angle of elevation of a jet plane from a point A on the ground is 60\(^\circ\). After a flight of 20 seconds at the speed of 432 km/hour, the angle of elevation changes to 30\(^\circ\). If the jet plane is flying at a constant height, t...

17Height And Distance

Let in a right angled triangle, the smallest angle be \(\theta\). If a triangle formed by taking the reciprocal of its sides is also a right angled triangle, then sin\(\theta\) is equal to :

18Height And Distance

A pole stands vertically inside a triangular park ABC. Let the angle of elevation of the top of the pole from each corner of the park be \({\pi \over 3}\). If the radius of the circumcircle of \(\Delta\)ABC is 2, then the height of the pol...

19Height And Distance

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 45o. After walking a distance of 80 meters towards the top, up a slope
inclined at an angle of 30o to the h...

INTEGER+4 / -02020

20Height And Distance

Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If
AD = 8 m, BC = 11 m and AB = 10 m; then the distance (in meters) of a point M on AB from the point
A such that MD2 + MC2 is minimum is ______.

INTEGER+4 / -02020

21Height And Distance

The angle of elevation of the summit of a
mountain from a point on the ground is 45°.
After climbing up one km towards the summit
at an inclination of 30° from the ground, the
angle of elevation of the summit is found to be
60°. Then the he...

22Height And Distance

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 :

23Height And Distance

Two poles standing on a horizontal ground are of
heights 5m and 10 m respectively. The line joining
their tops makes an angle of 15º with ground. Then
the distance (in m) between the poles, is :-

24Height And Distance

Two vertical poles of heights, 20 m and 80 m stand
a part on a horizontal plane. The height (in meters)
of the point of intersection of the lines joining the
top of each pole to the foot of the other, from this
horizontal plane is :

25Height And Distance

If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30o and the angle of depression of reflection of the cloud in the lake from P be 60o, then the height of the cloud (in meters) from
the surface of the lake is...

26Height And Distance

The angle of elevation of the top of a vertical tower standing on a horizontal plane is observed to be 45o from
a point A on the plane. Let B be the point 30 m vertically above the point A. If the angle of elevation of the
top of the tower ...

27Height And Distance

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

28Height And Distance

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\(\sqrt 2\) ) and cosec–1
(2\(\sqrt 2\) ) respectively,
th...