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 horizontal distance between two towers is $60 \mathrm{m}$. The angle of elevation of the top of the taller tower as seen from the top of the shorter one is $30^{\circ}$. If the height of the taller tower is $150 \mathrm{m}$, then find the height of the shorter tower.
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2.In the figure given below, AB is perpendicular to BD and is of length X metres. DC = 30 m, $\angle ADB = 30^{\circ}$ and $\angle ACB = 45^{\circ}$. Which labelled segment in the diagram corresponds to the expression $X\sqrt{3}$ derived from the tangent of $\angle ADB$?
- A.AB
- B.BD
- C.BC
- D.DC
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3.Two pillars of equal heights stand on either side of a roadway, which is 150 m wide. At a point in the roadway between the pillars the elevations of the tops of the pillars are 60° and 30°. What is the height of the pillars?
- A.37.5 m
- B.64.95 m
- C.86.60 m
- D.129.90 m
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4.From the top of a tower 100 m high, a man observes the angles of depression of two ships A and B, on opposite sides of the tower as 45° and 38° respectively. If the foot of the tower and the ships are in the same horizontal line, find the distance between the two ships A and B to the nearest metre.
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5.In the given diagram, two people are standing on the same side of a tower in a straight line with it. They measure the angles of elevation of the top of the tower as 25° and 50° respectively. If the height of the tower is 70 m, which labelled segment represents the distance between the two people?
- A.The segment from the base of the tower to the person with 25° angle
- B.The segment from the base of the tower to the person with 50° angle
- C.The segment between the two people (difference of their distances from the base)
- D.The vertical height of the tower itself
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