MCQOPTIONS
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MCQOPTIONS
This section includes 15 Mcqs, each offering curated multiple-choice questions to sharpen your GEOMETRY knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The distance between two vertical poles is 60 m. The height of one of the poles is double the height of the other. The angle of elevation of the top of the poles from the middle point of the line segment joining their feet are complementary to each other. The height of the poles are : |
| A. | 10 m and 20 m |
| B. | 20 m and 40 m |
| C. | 20.9 m and 41.8 m |
| D. | 15√2 m and 30√2 m |
| Answer» E. | |
| 2. |
A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30°. The man walks some distance towards the tower and then his angle of elevation of the top of the tower is 60°. If the height of the tower is 30 m, then the distance he moves is |
| A. | 22 m |
| B. | 22√3 m |
| C. | 20 m |
| D. | 20√3 m |
| Answer» B. 22√3 m | |
| 3. |
An aeroplane when flying at a height of 5000 m from the ground passes vertically above another aeroplane at an instant, when the angles of elevation of the two aeroplanes from the same point on the ground are 60° and 45° respectively. The vertical distance between the aeroplanes at that instant is |
| A. | 5000(√3 – 1) m |
| B. | 5000(3 – √3) m |
| C. | 5000{1 – (1 / √3)} m |
| D. | 4500 m |
| Answer» D. 4500 m | |
| 4. |
The angle of elevation of the top of a building and the top of the chimney on the roof of the building from a point on the ground are x° and 45° respectively. The height of building is h metre. Then the height of the chimney (in metre) is : |
| A. | h cot x + h |
| B. | h cot x – h |
| C. | h tan x – h |
| D. | h tan x + h |
| Answer» C. h tan x – h | |
| 5. |
At a point on a horizontal line through the base of a monument, the angle of elevation of the top of the monument is found to be such that its tangent is 1/5. On walking 138 metres towards the monument the secant of the angle of elevation is found to be 193/12. The height of the monument (in meter) is |
| A. | 35 |
| B. | 49 |
| C. | 42 |
| D. | 56 |
| Answer» D. 56 | |
| 6. |
The angle of elevation of the top of a tower from two points A and B lying on the horizontal through the foot of the tower are respectively 15° and 30°. If A and B are on the same side of the tower and AB = 48 metre, then the height of the tower is : |
| A. | 24√3 metre |
| B. | 24 metre |
| C. | 24√2 metre |
| D. | 96 metre |
| Answer» C. 24√2 metre | |
| 7. |
If the angle of elevation of the sun changes from 30° to 45°, the length of the shadow of a pillar decreases by 20 metres. The height of the pillar is |
| A. | 20(√3 – 1) m |
| B. | 20 (√3 + 1) m |
| C. | 10 (√3 – 1) m |
| D. | 10(√3 + 1) m |
| Answer» E. | |
| 8. |
From a point P on the ground the angles of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45° Find the length of the flagstaff. (Take √3 = 1.732) |
| A. | 10(√3 + 2) m |
| B. | 10(√3 + 1) m |
| C. | 10√3 m |
| D. | 7.32 m |
| Answer» E. | |
| 9. |
The shadow of a tower is 15 m when the sun’s elevation is 30°. What is the length of the shadow when the sun’s elevation is 60°? |
| A. | 3 m |
| B. | 4 m |
| C. | 5 m |
| D. | 6 m |
| Answer» D. 6 m | |
| 10. |
A telegraph post gets broken at a point against a storm and its top touches the ground at a distance 20 m from the base of the post making an angle 30° with the ground. What is the height of the post? |
| A. | 40/√3 m |
| B. | 20√3 m |
| C. | 40√3 m |
| D. | 30 m |
| Answer» C. 40√3 m | |
| 11. |
From the top of a cliff 90 m high, the angles of depression of the top and bottom of a tower are observed to be 30° and 60°, respectively. What is the height of the tower? |
| A. | 30 m |
| B. | 45 m |
| C. | 60 m |
| D. | 75 m |
| Answer» D. 75 m | |
| 12. |
The length of the shadow of a vertical tower on level ground increases by 10 metres when the altitude of the sun changes from 45° to 30°. Then the height of the tower is |
| A. | 5√3 metre |
| B. | 10(√3 + 1) metre |
| C. | 5(√3 + 1) metre |
| D. | 10√3 metre |
| Answer» B. 10(√3 + 1) metre | |
| 13. |
The angle of elevation of a tower from a distance 50 m from its foot is 30°. The height of the tower is |
| A. | 50√3 m |
| B. | 50 / √3 m |
| C. | 75√3 m |
| D. | 75 / √3 m |
| Answer» C. 75√3 m | |
| 14. |
The angle of elevation of a tower from a distance 100 m from its foot is 30°. Height of the tower is : |
| A. | (100 / √3) m |
| B. | (150 / √3) m |
| C. | (200 / √3) m |
| D. | 100√3 m |
| Answer» B. (150 / √3) m | |
| 15. |
The angle of elevation of the top of a tower from the point P and Q at distance of 'a' and 'b' respectively from the base of the tower and in the same straight line with it are complementary. The height of the tower is |
| A. | √ab |
| B. | a / b |
| C. | ab |
| D. | a2b2 |
| Answer» B. a / b | |