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.In the following diagram, AB is a floor-board; PQRS is a cubical box with each edge = 1 m and $\angle B = 60^{\circ}$. Calculate the length of the board AB.
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2.A boy 1.6 m tall can just see the sun over a wall 3.7 m high, which is 2.1 m away from him. Find the angle of elevation of the sun.
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3.The angle of elevation of the top of a tower is observed to be $60^{\circ}$. At a point, 30 m vertically above the first point of observation, the elevation is found to be $45^{\circ}$. Find: (i) the height of the tower, (ii) its horizontal distance from the points of observation.
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4.The angles of elevation of the top of a tower from the points $P$ and $Q$ at distance of $a$ and $b$ respectively from the base and in the same straight line with it, are complementary. The height of the tower is
- a.$ab$
- b.$\sqrt{ab}$
- c.$\sqrt{\frac{a}{b}}$
- d.$\sqrt{\frac{b}{a}}$
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5.A tree is broken by the wind. The top struck the ground at an angle of $30^{\circ}$ and at distance of 10 m from its root. The whole height of the tree is $(\sqrt{3} = 1.732)$
- a.$10\sqrt{3}\,\mathrm{m}$
- b.$3\sqrt{10}\,\mathrm{m}$
- c.$20\sqrt{3}\,\mathrm{m}$
- d.$3\sqrt{20}\,\mathrm{m}$
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