SSC CGL Trigonometry Verified Practice Test 4
15 structurally validated Trigonometry questions with unique options, mapped answers and explanations.
SSC CGL Trigonometry Verified Practice Test 4
15 structurally validated Trigonometry questions with unique options, mapped answers and explanations.
Preview all 15 questions in SSC CGL Trigonometry Verified Practice Test 4 (no login required)
- Ratio
1. If sin A = 5/13, then cot A is:
- A. 5/12
- B. 12/5 (Correct)
- C. 13/12
- D. 12/13
Explanation: Using a 5-12-13 triangle, cot A = 12/5.
- Identity
2. Which expression is equal to 1?
- A. tan² A - sec² A
- B. sec² A - tan² A (Correct)
- C. cosec² A + cot² A
- D. sin² A - cos² A
Explanation: sec² A - tan² A = 1.
- Applied Trigonometry
3. A kite is flying at a height of 30 m. If the string makes an angle of 30° with the ground, length of string is:
- A. 30 m
- B. 40 m
- C. 50 m
- D. 60 m (Correct)
Explanation: sin 30° = 30 / string, so the string is 60 m.
- Expression
4. If tan A = 1, then sec² A is:
- A. 1
- B. 2 (Correct)
- C. 3
- D. 4
Explanation: 1 + tan² A = sec² A, so sec² A = 2.
- Standard Angle
5. The value of cosec 45° is:
- A. √2 (Correct)
- B. 1/√2
- C. 1
- D. 2
Explanation: cosec 45° = √2.
- Complementary Angle
6. sec 62° is equal to:
- A. cosec 28° (Correct)
- B. sin 28°
- C. tan 28°
- D. cot 62°
Explanation: sec θ = cosec (90° - θ).
- Value Comparison
7. Which is greater?
- A. sin 45°
- B. cos 45°
- C. Both are equal (Correct)
- D. Cannot be compared
Explanation: sin 45° and cos 45° are both 1/√2.
- Applied Trigonometry
8. From the top of a 10 m wall, the angle of depression to a point on the ground is 45°. Distance of the point from the wall is:
- A. 5 m
- B. 10 m (Correct)
- C. 10√2 m
- D. 20 m
Explanation: Angle of depression equals angle of elevation. tan 45° = 10 / distance, so distance = 10 m.
- Ratio
9. If cos A = 15/17, then sin A equals:
- A. 8/17 (Correct)
- B. 15/8
- C. 17/8
- D. 8/15
Explanation: Using an 8-15-17 triangle, sin A = 8/17.
- Simplification
10. cos 60° / sin 30° equals:
- A. 1/2
- B. 1 (Correct)
- C. 2
- D. √3
Explanation: Both values are 1/2.
- Identity
11. If cot A = 1, then cosec² A equals:
- A. 1
- B. 2 (Correct)
- C. 3
- D. 4
Explanation: 1 + cot² A = cosec² A, so the answer is 2.
- Expression
12. If sin A = 12/13, then sec A is:
- A. 13/5 (Correct)
- B. 5/13
- C. 13/12
- D. 12/5
Explanation: With a 5-12-13 triangle, cos A = 5/13, so sec A = 13/5.
- Formula
13. The reciprocal of tan A is:
- A. sec A
- B. sin A
- C. cot A (Correct)
- D. cosec A
Explanation: cot A = 1 / tan A.
- Standard Angle
14. The value of cos 45° is:
- A. 1/2
- B. 1/√2 (Correct)
- C. √3/2
- D. 1
Explanation: cos 45° = 1/√2.
- Identity
15. If sec A = 2, then tan² A equals:
- A. 1
- B. 2
- C. 3 (Correct)
- D. 4
Explanation: sec² A = 4, so tan² A = 3.