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Mathematics - Heights and Distances

Practise 62 NTA Abhyas (JEE Main) questions on Heights and Distances. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Heights and Distances has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 62 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1A balloon moving in a straight line passes vertically above two points A and B on a horizontal plane 10 f t apart. When above A the balloon
  2. 2Two straight roads O A and O B intersect at O . A tower is situated within the angle formed by them and subtends angles of 45 o and 30 o at
  3. 3A B is a vertical tower. The point A is on the ground and C is the middle point of A B . The part C B subtend an angle α at a point P on the
  4. 4Each side of a square subtends an angle of 60 o at the top of a tower 5 meters high standing in the center of the square. If a meters is the
  5. 5A ladder 5 m long leans against a vertical wall. The bottom of the ladder is 3 m from the wall. If the bottom of the ladder is pulled 1 m fa
  6. 6A stationary balloon is observed from three points A , B and C on the plane ground and is found that its angle of elevation from each point
  7. 7A person standing at point P sees angle of elevation of the top of a building, whose base is 50 meters away, to be 60 o . Another building w
  8. 8Consider a cubical hall A B C D P Q R S with each side 20 m and base as A B C D . If G is the center of the wall B C R Q and T is the midpoi
  9. 9The tops of two poles of height 40 m and 25 m are connected by a wire of length 30 2 3 - 1 m . If the wire makes an angle α with the horizon
  10. 10A vertical tower subtends an angle of 60 o at a point on the same level as the foot of the tower. On moving 100 m further in line with the t
  11. 11Two poles of height a meters and b meters stand at the centres of two circular plots which touch each other externally at a point and the tw
  12. 12If from the top of a tower 80 meters high the angles of depression of the top and bottom of a house are 30 o and 45 o respectively, then the
  13. 13The length of the shadows of a vertical pole of height h , thrown by the sun's rays at three different moments are h , 2 h and 3 h . The sum
  14. 14If from the top of a tower, 60 metres high, the angles of depression of the top and floor of a house are 30 o and 60 o respectively, then th
  15. 15Let 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 al
  16. 16When the elevation of the sun changes from 45 o to 30 o , the shadow of a tower increases by 60 units, then the height of the tower is
  17. 17A tower leans towards west making an angle with the vertical. The angular elevation of B , the top most point of the tower, is 75 o as obser
  18. 18A tower A B leans towards west making an angle α with the vertical. The angular elevation of B , the top most point of the tower, is 6 0 o a
  19. 19Two poles standing on horizontal ground are of heights 10 meters 40 meters respectively. The line joining their tops makes an angle of 30 o
  20. 20Two vertical poles A L and B M of height 4 m and 16 m respectively stand apart on a horizontal plane. If A , B be the feet of the poles and
  21. 21Two poles standing on a horizontal ground are of heights x meters and 40 meters respectively. The line joining their tops makes an angle of
  22. 22Two ships are sailling in the sea on the two sides of a lighthouse. If the distance between the ships is 10 3 + 1 meters and their angle of
  23. 23A flagstaff stands vertically on a pillar, the height of the flagstaff being triple the height of the pillar. A man on the ground at a dista
  24. 24The angle of elevation of an object on a hill is observed from a certain point in the horizontal plane through its base, to be 30 . After wa
  25. 25A ladder rests against a vertical wall at an angle α to the horizontal. If the foot is pulled away through a distance 2 m , then it slides a
  26. 26The tops of two poles of heights 40 m and 25 m are connected by a wire. If the wire makes an angle 3 0 o with the horizontal, then the lengt
  27. 27Each side of a square subtends an angle of 60 ° at the top of a tower 5 meters high standing at the center of the square. If a meters is the
  28. 28An isosceles triangle made of wood of base 10 feet and height 8 feet is placed vertically with its base on the ground and vertex directly ab
  29. 29If 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 °
  30. 30An observer finds that the angular elevation of a tower is θ . On advancing 3 m towards the tower, the elevation is 45 o and on advancing 2
  31. 31A 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 ang
  32. 32A vertical tower subtends an angle of 60 o at a point on the same level as the foot of the tower. On moving 100 m further from the first poi
  33. 33A statue of height 4 m stands on a tower of height 10 m . The angle subtended by the statue at the eyes of an observer of height 2 m , stand
  34. 34From the top of a tower, of 100 m height, the angles of depression of two objects, 200 3 m apart on the horizontal plane on a line passing t
  35. 35A flagstaff stands vertically on a pillar, the height of the flagstaff being double the height of the pillar. A man on the ground at a dista
  36. 36At the foot of the mountain, the angle of elevation of its summit is 45 o , after ascending 1000 m towards the mountain up a slope of 30 o i
  37. 37P Q R is a triangular park with P Q = P R = 200 m . A TV tower stands at the mid-point of Q R . If the angles of elevation of the top of the
  38. 38Two vertical poles of height 10 m and 40 m stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lin
  39. 39A balloon is rising vertically upwards. At an instant, an observer on the ground, whose distance from the balloon is 100 meters, sees the ba
  40. 40The angular elevation of tower C D at a point A due south of it is 60 o and at a point B due west of A , the elevation is 3 0 o . If A B = 5
  41. 41A tower subtends an angle 75 o at a point on the same level as the foot of the tower and at another point, 10 meters above the first, the an
  42. 42Two men are on the opposite sides of a tower. They measure the angles of elevation of the top of the tower as 45 o and 30 o respectively. If
  43. 43If a tower subtends equal angles at four points P , Q , R and S that lie in a plane containing the foot of the tower, then which of the foll
  44. 44An isosceles triangle of wood of base 10 feet and height 8 3 feet is placed vertically with its base on the ground and vertex directly above
  45. 45Two poles of height 10 meters and 20 meters stand at the centres of two circular plots which touch each other externally at a point and the
  46. 46The angular depressions of the top and the foot of a tower, as seen from the top of a second tower which is 150 meters high and standing on
  47. 47An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60 o and after 10 seconds the elevation is observed to
  48. 48A tower subtends angles α , 2 α and 3 α respectively at points, A , B and C (all points lying on the same side on a horizontal line through
  49. 49A flag - staff of 5 meters high stands on a building of 25 meters height. For an observer at a height of 30 meters, the flag-staff and the b
  50. 50The angle of elevation of a cloud from a point 250 m above a lake is 15 o and angle of depression of its reflection in the lake is 45 o . Th

Frequently Asked Questions

1.How many questions are available for Heights and Distances?

This chapter includes 62 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

These are NTA Abhyas (JEE Main) questions specifically for the Heights and Distances chapter. Questions from other exams like JEE Main or JEE Advanced are organised separately under their respective exam sections.

3.What is the difficulty level of Heights and Distances questions in NTA Abhyas (JEE Main)?

Of the 62 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Heights and Distances should I focus on?

All of this chapter's questions come from a single topic: Uncategorized.