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Mathematics - Heights and Distances

Practise 47 JEE Main previous year questions on Heights and Distances, compiled from papers spanning 2003 to 2023. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Main tests.

Heights and Distances has been asked in 17 of the 25 years of JEE Main papers analysed (2002–2026), with 47 questions in all. 62% of them were easy, 28% moderate and 11% tough. Most of its questions came from 2022, with 7 questions that year. In the last three years (2024–2026) it had 0 questions across 49 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Heights and Distances.

  1. 1The angle of elevation of the top P of a tower from the feet of one person standing due south of the tower is 45 and from the feet of anothe11 Apr, 2023 (E)Heights and Distances
  2. 2From the top A of a vertical wall A B of height 30 m , the angles of depression of the top P and bottom Q of a vertical tower P Q are 15 and06 Apr, 2023 (M)Heights and Distances
  3. 3The angle of elevation of the top of a tower from a point A due north of it is and from a point B at a distance of 9 units due west of A is 29 Jul, 2022 (M)Heights and Distances
  4. 4A horizontal park is in the shape of a triangle O A B with A B = 16 . A vertical lamp post O P is erected at the point O such that P A O = P28 Jul, 2022 (E)Heights and Distances
  5. 5Let 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 to27 Jul, 2022 (M)Heights and Distances
  6. 6The 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 on27 Jul, 2022 (E)Heights and Distances
  7. 7A 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 fr25 Jul, 2022 (M)Heights and Distances
  8. 8From 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 of29 Jun, 2022 (E)Heights and Distances
  9. 9Let 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 poles28 Jun, 2022 (M)Heights and Distances
  10. 10A 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. If31 Aug, 2021 (M)Heights and Distances
  11. 11Two poles A B of length a metres and C D of length a + b ( b a ) metres are erected at the same horizontal level with bases at B and D . If 27 Aug, 2021 (E)Heights and Distances
  12. 12A 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 from25 Jul, 2021 (M)Heights and Distances
  13. 13A pole stands vertically inside a triangular park A B C . Let the angle of elevation of the top of the pole from each corner of the park be 18 Mar, 2021 (E)Heights and Distances
  14. 14A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A , with uniform speed. At that point, a25 Feb, 2021 (M)Heights and Distances
  15. 15Two 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 thei24 Feb, 2021 (M)Heights and Distances
  16. 16The 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 of 432 km / hour , the 24 Feb, 2021 (E)Heights and Distances
  17. 17The 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 . Af06 Sep, 2020 (M)Heights and Distances
  18. 18The 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 incl06 Sep, 2020 (E)Heights and Distances
  19. 19Two vertical poles A B = 15 m and C D = 10 m are standing apart on a horizontal ground with points A and C on the ground. If P is the point 04 Sep, 2020 (M)Heights and Distances
  20. 20The angle of elevation of a cloud C from a point P , 200 m above a still take is 30 o . If the angle of depression of the image of C in the 04 Sep, 2020 (E)Heights and Distances
  21. 21The angle of the top of a vertical tower standing on a horizontal plane is observed to be 45 from a point A on the plane. Let B be the point12 Apr, 2019 (E)Heights and Distances
  22. 22A B C is a triangular park with A B = A C = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of t10 Apr, 2019 (M)Heights and Distances
  23. 23Two poles standing on a horizontal ground are of heights 5 m and 10 m respectively. The line joining their tops makes an angle of 15 with th09 Apr, 2019 (E)Heights and Distances
  24. 24Two vertical poles of height, 20 m and 80 m stand apart on a horizontal plane. The height (in meters) of the point of intersection of the li08 Apr, 2019 (E)Heights and Distances
  25. 25If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30 o and the angle of depression of reflection of the coul12 Jan, 2019 (E)Heights and Distances
  26. 26Consider a triangular plot A B C with sides A B = 7 m , B C = 5 m and C A = 6 m . A vertical lamp-post at the mid-point D of A C subtends an10 Jan, 2019 (M)Heights and Distances
  27. 27A 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 for16 Apr, 2018 (Online)Heights and Distances
  28. 28An aeroplane flying at a constant speed, parallel to the horizontal ground, above it, is observed at an elevation of from a point on the gro15 Apr, 2018 (Shift 1 Online)Heights and Distances
  29. 29A tower of height is located exactly opposite to a tower of height on a straight road. From the top of , if the angle of depression of the f15 Apr, 2018 (Shift 2 Online)Heights and Distances
  30. 30An aeroplane flying at a constant speed, parallel to the horizontal ground, 3 km above it is observed at an elevation of 60 from a point on 15 Apr, 2018Heights and Distances
  31. 31P Q R is a triangular park with P Q = P R = 200 m . A T.V. tower stands at the mid-point of Q R . If the angles of elevation of the top of t08 Apr, 2018Heights and Distances
  32. 32Let a vertical tower A B have its end A on the level ground. Let C be the mid-point of A B and P be a point on the ground such that A P = 2 02 Apr, 2017Heights and Distances
  33. 33The angle of elevation of the top of a vertical tower from a point A, due east of it is 45 o . The angle of elevation of the top of the same10 Apr, 2016 (Online)Heights and Distances
  34. 34A 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 an03 Apr, 2016Heights and Distances
  35. 35Let 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 11 Apr, 2015 (Online)Heights and Distances
  36. 36If 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 ,04 Apr, 2015Heights and Distances
  37. 37Two ships A and B are sailing straight away from a fixed point along routes such that is always . At a certain instance, and the ship is sai11 Apr, 2014 (Online)Heights and Distances
  38. 38The angle of elevation of the top of a vertical tower from a point on the horizontal ground was observed to be . After moving a distance 2 m11 Apr, 2014 (Online)Heights and Distances
  39. 39A 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 s06 Apr, 2014Heights and Distances
  40. 40A B C D is a trapezium such that A B and C D are parallel and B C C D . If A D B = , B C = p and C D = q , then A B is equal to07 Apr, 2013Heights and Distances
  41. 41If two vertical poles and high stand apart on a horizontal plane, then the height (in ) of the point of intersection of the lines joining th07 May, 2012 (Online)Heights and Distances
  42. 42is a vertical pole with at the ground level and at the top. man finds that the angle of elevation of the point from a certain point on the g2008Heights and Distances
  43. 43A tower stands at the centre of a circular park. and are two points on the boundary of the park such that subtends an angle of at the foot o2007Heights and Distances
  44. 44A lizard, at an initial distance of behind an insect, moves from rest with an acceleration of and pursues the insect which is crawling unifo2005Heights and Distances
  45. 45A 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 and 2004Heights and Distances
  46. 46A particle moves towards east from a point to a point at the rate of and then towards north from to at the rate of . If and , then its avera2004Heights and Distances
  47. 47The upper th portion of a vertical pole subtends an angle at a point in the horizontal plane through its foot and at a distance from the foo2003Heights and Distances

Frequently Asked Questions

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

This chapter includes 47 questions compiled from JEE Main papers spanning 2003 to 2023.

2.Are these questions only from JEE Main, or from other exams too?

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

3.Is Heights and Distances an important chapter for JEE Main Mathematics?

Heights and Distances has appeared in 17 of the 25 years of JEE Main papers covered here, with 47 questions across 45 papers - about one per paper it appears in.

4.What is the difficulty level of Heights and Distances questions in JEE Main?

Of the 47 questions analysed for this chapter, 62% are easy, 28% moderate and 11% tough. 2022 had the most, with 7 questions.

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

All of this chapter's questions come from a single topic: Heights and Distances.

6.Is Heights and Distances's weightage in JEE Main going up or down?

Across all 45 papers analysed, Heights and Distances has averaged about 1.0 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.