Heights and Distances
41 CDS Mathematics previous year questions (PYQs) from 19 papers, 2016 to 2026, with answers and worked solutions.
About this chapter
- Difficulty: 1 easy · 26 moderate · 14 hard.
- Most-asked subtopics: Two Points of Observation (19), Observer Above the Ground (9), Towers on Plane Figures and Bearings (7).
- Updated 20 September 2026.
#1One Line of Sight
#2One Line of Sight
#3One Line of Sight
#4One Line of Sight
#5One Line of Sight
Done a few? Here’s your next move
#6One Line of Sight
#7Two Points of Observation
#8Two Points of Observation
#9Two Points of Observation
#10Two Points of Observation
#11Two Points of Observation
#12Two Points of Observation
#13Two Points of Observation
#14Two Points of Observation
#15Two Points of Observation
#16Two Points of Observation
- Set · 2 questionsConsider the following for the next two (02) items that follow : A flagstaff stands on the top of a vertical tower. The angle of elevation of the top of the flagstaff from a certain place on the same horizontal level with the base of the tower is found to be . Advancing a distance d towards the tower in the same horizontal plane, the angle of elevation of the top of the flagstaff is observed to be and that of the top of the tower is observed to be . Let H be the height of the top of the flagstaff from the base of the tower and h be the height of the tower.
#17Two Points of Observation
#18Two Points of Observation
- Set · 2 questionsAB is a straight road leading to the foot P of a tower of height h. Q is at distance x from P and R is at a distance y from Q (R is farther from P than Q; R, Q are on the same side). The angle of elevation of the top of the tower at Q is twice of that at R. (Use the formula )
#19Two Points of Observation
#20Two Points of Observation
#21Two Points of Observation
#22Two Points of Observation
#23Two Points of Observation
#24Two Points of Observation
#25Two Points of Observation
#26Observer Above the Ground
#27Observer Above the Ground
#28Observer Above the Ground
#29Observer Above the Ground
#30Observer Above the Ground
- Set · 2 questionsConsider the following for the next two (02) items that follow : The angle of elevation of a cloud at C from a point (P), H metres above the surface of a lake is . The height of the cloud from the surface of the lake is 2H metres. Let be the angle of depression of the reflection of the cloud in the lake from the point P.
#31Observer Above the Ground
#32Observer Above the Ground
#33Observer Above the Ground
#34Observer Above the Ground
#35Towers on Plane Figures and Bearings
#36Towers on Plane Figures and Bearings
#37Towers on Plane Figures and Bearings
#38Towers on Plane Figures and Bearings
#39Towers on Plane Figures and Bearings
#40Towers on Plane Figures and Bearings
#41Towers on Plane Figures and Bearings
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