Class 10 Mathematics (NCERT)

1. The angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level is called:

• A. Angle of depression
• B. Angle of elevation
• C. Obtuse angle
• D. Acute angle

2. If a tower is 30 m high and the angle of elevation of its top from a point on the ground is 45°, the distance of the point from the base of the tower is:

• A. 15 m
• B. 30 m
• C. 30√3 m
• D. 15√3 m

3. A pole 6 m high casts a shadow 2√3 m long on the ground, then the Sun's elevation is:

• A. 60°
• B. 45°
• C. 30°
• D. 90°

4. If the height of a vertical pole and the length of its shadow on the ground are equal, then the angle of elevation of the Sun is:

• A. 30°
• B. 45°
• C. 60°
• D. 90°

5. The angle of depression of an object on the ground from the top of a 75 m high cliff is 30°. The distance of the object from the foot of the cliff is:

• A. 75 m
• B. 75√3 m
• C. 25√3 m
• D. 150 m

6. A ladder 10 m long reaches a window 8 m above the ground. The distance of the foot of the ladder from the base of the wall is:

• A. 2 m
• B. 4 m
• C. 6 m
• D. 8 m

7. A kite is flying at a height of 60 m above the ground attached to a string inclined at 60° to the horizontal. Assuming string is straight, its length is:

• A. 40√3 m
• B. 30√3 m
• C. 120 m
• D. 80 m

8. If the angle of elevation of the top of a tower from a point on the ground is 30° and on walking 20 m towards the tower it becomes 60°, the height of tower is:

• A. 10 m
• B. 10√3 m
• C. 20√3 m
• D. 30 m

9. The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30° than when it is 60°. The height of the tower is:

• A. 20√3 m
• B. 40√3 m
• C. 10√3 m
• D. 20 m

10. Line of sight is the line drawn from the eye of an observer to the:

• A. Top of the object
• B. Point in the object viewed by the observer
• C. Base of the object
• D. Horizontal plane

11. A 1.5 m tall observer is 28.5 m away from a chimney. The angle of elevation of top of chimney from her eyes is 45°. Height of chimney is:

• A. 28.5 m
• B. 30 m
• C. 27 m
• D. 31.5 m

12. The angle of elevation of the top of a building from the foot of a tower is 30° and from top of building to foot of tower is 60°. If tower is 50 m high, height of building is:

• A. 16.67 m
• B. 25 m
• C. 50/3 m
• D. Both A and C

13. The angle of elevation of the Sun increases from 30° to 60°, the length of shadow of a tower:

• A. Increases
• B. Decreases
• C. Remains same
• D. Doubles

14. An observer on top of a 100 m high lighthouse sees a boat at an angle of depression of 30°. Distance of boat from lighthouse base is:

• A. 100 m
• B. 100/√3 m
• C. 100√3 m
• D. 200 m

15. If a ratio of length of a rod and its shadow is 1 : √3, then the angle of elevation of the sun is:

• A. 30°
• B. 45°
• C. 60°
• D. 90°

16. A circus artist is climbing a 20 m long rope tightly stretched from top of a vertical pole to ground. If angle made with ground is 30°, height of pole is:

• A. 10 m
• B. 20 m
• C. 10√3 m
• D. 5 m

17. A tree breaks due to a storm and the broken top touches ground making an angle of 30° with it. Distance from foot to top touching ground is 8 m. Total height of tree is:

• A. 8√3 m
• B. 8/√3 m
• C. 16/√3 m
• D. 24 m

18. The tops of two poles of height 20 m and 14 m are connected by a wire. If wire makes an angle of 30° with horizontal, length of wire is:

• A. 6 m
• B. 8 m
• C. 10 m
• D. 12 m

19. From a point P on level ground, the angle of elevation of top of a tower is 30°. If tower is 100 m high, distance of P from top of tower is:

• A. 100 m
• B. 200 m
• C. 100√3 m
• D. 50 m

20. The angle of elevation of top of a tower from two points at distances 'a' and 'b' from base and in same line are complementary. Height of tower is:

• A. ab
• B. √(a/b)
• C. √(ab)
• D. a/b

21. Angle of elevation of top of a building from a point 50 m away from its foot is 60°. Height of building is:

• A. 50 m
• B. 50√3 m
• C. 50/√3 m
• D. 25√3 m

22. If two towers of height h1 and h2 subtend angles of 60° and 30° respectively at mid-point of line joining their feet, then h1 : h2 is:

• A. 1 : 2
• B. 1 : 3
• C. 3 : 1
• D. 2 : 1

23. When object is below horizontal level, angle between line of sight and horizontal line is called:

• A. Angle of elevation
• B. Angle of depression
• C. Right angle
• D. Straight angle

24. A cable tower of height 7 m has top of a building at angle of elevation 60° and foot at depression 45°. Height of tower is:

• A. 7(√3 + 1) m
• B. 7(√3 - 1) m
• C. 14 m
• D. 7√3 m

25. A statue 1.6 m tall stands on top of a pedestal. From a point on ground, elevation of top of statue is 60° and top of pedestal is 45°. Height of pedestal is:

• A. 0.8(√3 + 1) m
• B. 0.8(√3 - 1) m
• C. 1.6(√3 + 1) m
• D. 1.6(√3 - 1) m

26. If the shadow of a tower is 1/√3 times its height, then the angle of elevation of the sun is:

• A. 30°
• B. 45°
• C. 60°
• D. 90°

27. An observer 1.7 m tall stands 20 m away from a tower 21.7 m high. The angle of elevation of top of tower from observer's eye is:

• A. 30°
• B. 45°
• C. 60°
• D. 0°

28. The angle of depression of a car parked on road from top of 150 m tower is 30°. Distance of car from tower is:

• A. 150 m
• B. 150√3 m
• C. 75√3 m
• D. 150/√3 m

29. Length of shadow of a tree is equal to its height when angle of elevation of Sun is:

• A. 0°
• B. 30°
• C. 45°
• D. 60°

30. From a point 30 m away from base of a vertical structure, elevation of top is 30°. Height of structure is:

• A. 10√3 m
• B. 30√3 m
• C. 15 m
• D. 10 m