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 length of the shadow of a vertical tower is √3 times its height. Find the angle of elevation of the sun.
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2.From the top of a cliff, 60 metres high, the angles of depression of the top and bottom of a tower are observed to be $30^{\circ}$ and $60^{\circ}$. Find the height of the tower.
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3.The shadow of a vertical tower on a level ground increases by 10 m, when the altitude of the sun changes from 45° to 30°. What is the height of the tower correct to two decimal places?
- A.10 m
- B.13.66 m
- C.20 m
- D.27.32 m
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4.The shadow of a tower on level ground is 40 m longer when the Sun's altitude is $30^{\circ}$ than when it is $60^{\circ}$. What is the height of the tower?
- A.$10\sqrt{3} \mathrm{m}$
- B.$20\sqrt{3} \mathrm{m}$
- C.$30\sqrt{3} \mathrm{m}$
- D.$40\sqrt{3} \mathrm{m}$
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5.A man on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is 60°. When he moves 20 m away from the bank, the angle of elevation becomes 30°. What is the height of the tree?
- A.5√3 m
- B.10√3 m
- C.15√3 m
- D.20√3 m
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