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 tower at a distance of 120 m from its foot on a horizontal plane is found to be 30°. Find the height of the tower.
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2.Two vertical poles are on either side of a road. A 30 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes angle 32°24′ with the pole and when it is turned to rest against another pole, it makes angle 32°24′ with the road. Calculate the width of the road.
- A.41.36 m
- B.45.36 m
- C.51.36 m
- D.30.00 m
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3.A kite is flying at a height of 90 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. What is the length of the string, assuming there is no slack in the string?
- A.90 m
- B.60√3 m
- C.180 m
- D.30√3 m
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4.An observer finds the angle of elevation of the top of the tower from a certain point on the ground as 30°. If the observer moves 20 m towards the base of the tower, the angle of elevation of the top increases by 15°. What is the height of the tower?
- A.10(√3 - 1) m
- B.10(√3 + 1) m
- C.20(√3 + 1) m
- D.20(√3 - 1) m
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5.The tops of two towers of height $x$ and $y$ on level ground subtend angles of $30^{\circ}$ and $60^{\circ}$ respectively at the centre of the line joining their feet. What is the ratio $x:y$?
- A.$1:2$
- B.$1:3$
- C.$2:3$
- D.$3:1$
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