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NDA Heights and Distances PYQs with Solutions

26 previous year questions from Heights and Distances (NDA Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

26 questionsMathematics2013–2026Answers + solutions

About Heights and Distances PYQs

Heights and Distances has 26 previous year questions in the Quantrex Academy NDA Mathematics bank. The 26 questions in this list come from NDA (26), spanning 2013 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

NDA Heights and Distances PYQs with Solutions

About Heights and Distances PYQs

Questions by year (this list)

Heights and Distances questions with solutions

A plane is observed to be approaching the airport. It is at a distance of 10 km from the point of observation and makes an angle of elevation of 67·5^ ^ ∘ . What is the height of

Consider the following for the two (02) items that follow: The top (M ) of a tower is observed from three points P , Q and R lying in a horizontal straight line which passes

A man at M , standing 100 m away from the base (P ) of a chimney of height 50 m, observes the angle of elevation of the highest point (Q ) of the smoke to be 45° . The highest

Consider the following for the two (02) items that follow: The top (M ) of a tower is observed from three points P , Q and R lying in a horizontal straight line which passes

Paragraph: A flagstaff 20 m long standing on a pillar 10 m high subtends an angle ^ -1 (0.5) at a point P on the ground. Let θ be the angle subtended by the pillar at this point P

Paragraph: There are two points P and Q due south of a leaning tower, which leans towards north. P is at a distance x and Q is at a distance y from the foot of the tower (x > y) .

Paragraph: There are two points P and Q due south of a leaning tower, which leans towards north. P is at a distance x and Q is at a distance y from the foot of the tower (x > y) .

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h . At a point on the plane the angles of elevation of the bottom and top of the

Paragraph: There are two points P and Q due south of a leaning tower, which leans towards north. P is at a distance x and Q is at a distance y from the foot of the tower (x > y) .

A ladder 6 m long reaches a point 6 m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the top of the flagstaff is 75^ ^ ∘ . What is the height

The shadow of a tower is found to be x metre longer, when the angle of elevation of the sun changes from 60^ ^ ∘ to 45^ ^ ∘ . If the height of the tower is 5(3+ 3 ) m , then what

The angle of elevation of a tower of height h from a point A due South of it is x and from a point B due East of A is y. If AB=z , then which one of the following is correct ?

A ladder 9 m long reaches a point 9 m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the flagstaff is 60^ ^ ∘ . What is the height of the

A balloon is directly above one end of a bridge. The angle of depression of the other end of the bridge from the balloon is 48^ ^ ∘ . If the height of the balloon above the bridge

The top of a hill observed from the top and bottom of a building of height h is at angles of elevation (π)/(6) and (π)/(3) respectively. What is the height of the hill?

If a flag-staff of 6 m height placed on the top of a tower throws a shadow of 2 3 m along the ground, then what is the angle that the sun makes with the ground?

A spherical balloon of radius r subtends an angle α at the eye of an observer, while the angle of elevation of its centre is β . What is the height of the centre of the balloon

The angles of elevation of the top of a tower from the top and foot of a pole are respectively 30^ ^ ∘ and 45^ ^ ∘ . If h_ T is the height of the tower and h_p is the height of

From the top of a lighthouse, 100 m high, the angle of depression of a boat is ^ -1 ((5)/(12)). What is the distance between the boat and the lighthouse?

A moving boat is observed from the top of a cliff of 150 m height. The angle of depression of the boat changes from 60^ ^ ∘ to 45^ ^ ∘ in 2 minutes. What is the speed of the boat

Two poles are 10 m and 20 m high. The line joining their tops makes an angle of 15^ ^ ∘ with the horizontal. The distance between the poles is approximately equal to

The angles of elevation of the top of a tower standing on a horizontal plane from two points on a line passing through the foot of the tower at distances 49 m and 36 m are 43^ ^ ∘

The angle of elevation of the top of a tower from a point 20 m away from its base is 45^ ^ ∘ . What is the height of the tower?

A lamp post stands on a horizontal plane. From a point situated at a distance 150 m from its foot, the angle of elevation of the top is 30^ ^ ∘ . What is the height of the lamp

From an aeroplane above a straight road the angles of depression of two positions at a distance 20 m apart on the road are observed to be 30^ ^ ∘ and 45^ ^ ∘ . The height of the

The angles of elevation of the top of a tower from two places situated at distances 21 m and x m from the base of the tower are 45^ ^ ∘ and 60^ ^ ∘ respectively. What is the value

Related NDA Mathematics chapters

Heights and Distances in other exams