ICSE Class 10 Heights and Distances — Mock Test (2027)
Free online mock test for Heights and Distances (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.
What to expect: This mock test covers key concepts from the Heights and Distances chapter — including application-based and competency-focused questions aligned with how ICSE actually sets the paper.
Tip: Attempt without notes first to identify gaps, then review explanations for any wrong answers. Retake after a few days for best retention.
Sample questions
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1.The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building.
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2.Two men standing on opposite sides of a tower measure the angles of elevation of the top of the tower as 30° and 60° respectively. If the height of the tower is 20 m, what is the distance between the two men?
- A.20√3 m
- B.40√3 m
- C.(80√3)/3 m
- D.60√3 m
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3.In the given diagram,
, from a window A, 10 m above the ground, the angle of elevation of the top C of a tower is x°, where tan x = 5/2, and the angle of depression of the foot D of the tower is y°, where tan y = 1/4. Which labelled segment corresponds to the height CD of the tower?- A.The vertical distance from point A to point C
- B.The vertical distance from point D to point C
- C.The horizontal distance from point A to point D
- D.The slant distance from point A to point C
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4.A man in a boat rowing away from a light house 150 m high, takes 1.5 minutes to change the angle of elevation of the top of the lighthouse from $60^{\circ}$ to $45^{\circ}$. Find the speed of the boat.
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5.A man on the bank of a river observes a tree on the opposite bank subtending an angle of 60° with its base. On moving 50 m away from the bank, the angle reduces to 30°. What is the height of the tree?
- A.25 m
- B.25√3 m
- C.43.3 m
- D.50 m
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