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.

Sample questions

1. 1.A man 1·8 m tall stands at a distance of 3·6 m from a lamp post and casts a shadow of 5·4 m on the ground. Find the height of the lamp post.
2. 2.11. Two climbers are at points A and B on a vertical cliff face. To an observer C, 40 m from the foot of the cliff, on the level ground, A is at an elevation of 48° and B of 57°. What is the distance between the climbers?
3. 3.Assertion : In the figure, if $BC = 20\mathrm{m}$, then height $AB$ is $11.56\mathrm{m}$. Reason: $\tan \theta = \frac{AB}{BC} = \frac{\text{perpendicular}}{\text{base}}$ where $\theta$ is the angle $\angle ACB$. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true.
   • A.Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
   • B.Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
   • C.Assertion (A) is true but reason (R) is false.
   • D.Assertion (A) is false but reason (R) is true.
4. 4.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
5. 5.The length of the shadow of a vertical tower is √3 times its height. Find the angle of elevation of the sun.