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.An aeroplane flying horizontally 1 km above the ground and going away from the observer is observed at an elevation of $60^{\circ}$. After 10 seconds, its elevation is observed to be $30^{\circ}$; find the uniform speed of the aeroplane in km per hour.
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2.A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon will the car reach the observation tower from this point?
- A.12.00 minutes
- B.16.39 minutes
- C.18.50 minutes
- D.20.00 minutes
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3.An aeroplane is flying horizontally with a speed of $173.2 \text{ m/sec}$, at a height of $3000 \text{ m}$. Find the time it would take for the angle of elevation of the plane as seen from a point on the ground to change from $60^{\circ}$ to $30^{\circ}$.
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4.An aeroplane is flying horizontally with a speed of $173.2 \text{ m/sec}$, at a height of $3000 \text{ m}$. The diagram below shows the positions of the plane when the angle of elevation from a point on the ground changes from $60^{\circ}$ to $30^{\circ}$. What is the label of the segment that represents the horizontal distance covered by the plane during this change?
- A.AB (the initial horizontal distance from the point to the plane)
- B.AE (the final horizontal distance from the point to the plane)
- C.CD (the difference between AE and AB)
- D.AC (the vertical height of the plane)
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5.An aeroplane at an altitude of 250 m observes the angles of depression of two boats on the opposite banks of a river to be 45° and 60°, respectively. The width of the river, correct to the nearest whole number, is:
- A.250 m
- B.350 m
- C.394 m
- D.450 m
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