Trigonometry · SSC CGL previous year questions

2023 85 questions

1. Q642023 · 19 Jul 2023 · Shift 4

   If sin θ - cos θ = 0, then find the value of (sin3 θ - cos3 θ).

   
   1. A.Option 1
   2. B.Option 2
   3. C.Option 3
   4. D.Option 4
   Show answer

   Answer: A

2. Q582023 · 18 Jul 2023 · Shift 1

   Using trigonometric formulas, find the value of

   
   1. A.-2
   2. B.2
   3. C.0
   4. D.1
   Show answer

   Answer: D

3. Q672023 · 18 Jul 2023 · Shift 1

   If , then the value of (sin A + cos A) × cosec A is _______.

   
   1. A.Option 1
   2. B.Option 2
   3. C.Option 3
   4. D.Option 4
   Show answer

   Answer: B

4. Q522023 · 18 Jul 2023 · Shift 2

   If sec θ + tan θ = 5, then find the value of tan θ.

   
   1. A.Option 1
   2. B.Option 2
   3. C.Option 3
   4. D.Option 4
   Show answer

   Answer: D

5. Q582023 · 18 Jul 2023 · Shift 2

   Simplify the following: sin 2x + 2 sin 4x + sin 6x

   1. A.4 cos2 x sin 4x
   2. B.4 cos2 x sin x
   3. C.2 cos2 x sin 4x
   4. D.4 sin2 x sin 4x
   Show answer

   Answer: A

6. Q712023 · 18 Jul 2023 · Shift 2

   If , A lies in III quadrant, the value of sec A is:

   
   1. A.Option 1
   2. B.Option 2
   3. C.Option 3
   4. D.Option 4
   Show answer

   Answer: B

7. Q752023 · 18 Jul 2023 · Shift 2

   The cost of 32 pens and 12 pencils is Rs. 790. What is the total cost (in Rs.) of 8 pens and 3 pencils together?

   1. A.200.5
   2. B.197.5
   3. C.180.5
   4. D.220.5
   Show answer

   Answer: B

8. Q652023 · 18 Jul 2023 · Shift 3

   If in ΔXYZ, XY = 4 and XZ = 5 cm, and Q is a point on YZ such that XQ bisects ∠X, then YQ ∶ QZ is:

   1. A.2 ∶ 3
   2. B.3 ∶ 2
   3. C.5 ∶ 4
   4. D.4 ∶ 5
   Show answer

   Answer: D

9. Q682023 · 18 Jul 2023 · Shift 3

   Find the value of the following expression. 12(sin4 θ + cos4 θ) + 18(sin6 θ + cos6 θ) + 78 sin2 θ cos2 θ

   1. A.30
   2. B.40
   3. C.10
   4. D.20
   Show answer

   Answer: A

10. Q722023 · 18 Jul 2023 · Shift 3

    If the cost of 120 m of cloth is Rs. 9,600, then what will be the cost of 147 m of that cloth?

    1. A.Rs. 16,170
    2. B.Rs. 11,670
    3. C.Rs. 11,760
    4. D.Rs. 17,160
    Show answer

    Answer: C

11. Q572023 · 18 Jul 2023 · Shift 4

    Find the value of the given expression. $\frac{4}{3}{\tan }^{2}45^{\circ }+3{\cos }^{2}30^{\circ }-2{\sec }^{2}30^{\circ }-\frac{3}{4}{\cot }^{2}60^{\circ }$

    1. A.Option 1
    2. B.Option 2
    3. C.Option 3
    4. D.Option 4
    Show answer

    Answer: A

12. Q642023 · 18 Jul 2023 · Shift 4

    Find the exact value of cos 120°.

    1. A.-0.5
    2. B.0
    3. C.0.5
    4. D.1
    Show answer

    Answer: A

13. Q702023 · 18 Jul 2023 · Shift 4

    Using tan (A - B) = , find the value of tan15°.

    
    1. A.+ 1
    2. B.- 1
    3. C.2 -
    4. D.2 +
    Show answer

    Answer: C

14. Q582023 · 17 Jul 2023 · Shift 1

    If sin t + cos t = , then find sin t. cos t.

    
    1. A.Option 1
    2. B.Option 2
    3. C.Option 3
    4. D.Option 4
    Show answer

    Answer: B

15. Q692023 · 17 Jul 2023 · Shift 1

    Find the value of sin2 25 + sin2 65.

    
    1. A.Option 1
    2. B.Option 2
    3. C.Option 3
    4. D.Option 4
    Show answer

    Answer: D

16. Q552023 · 17 Jul 2023 · Shift 2

    Find the value of cos 47° sec 133° + sin 44° cosec 136°.

    
    1. A.Option 1
    2. B.Option 2
    3. C.Option 3
    4. D.Option 4
    Show answer

    Answer: C

17. Q662023 · 17 Jul 2023 · Shift 2

    If $\tan \frac{\pi }{6}+\sec \frac{\pi }{6}=x$, then find x.

    1. A.Option 1
    2. B.Option 2
    3. C.Option 3
    4. D.Option 4
    Show answer

    Answer: A

18. Q742023 · 17 Jul 2023 · Shift 2

    If Sin θ = , find the value of tan θ - Cot θ.

    
    1. A.Option 1
    2. B.Option 2
    3. C.Option 3
    4. D.Option 4
    Show answer

    Answer: C

19. Q512023 · 17 Jul 2023 · Shift 3

    If a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 - q2 is equal to ______.

    1. A.a2 + b2
    2. B.a2 - b2
    3. C.b2 - a2
    4. D.b - a
    Show answer

    Answer: C

20. Q682023 · 17 Jul 2023 · Shift 3

    If , x lies in third quadrant, then tan x = ?

    
    1. A.Option 1
    2. B.Option 2
    3. C.Option 3
    4. D.Option 4
    Show answer

    Answer: A

21. Q702023 · 17 Jul 2023 · Shift 3

    Using cos(A + B) = cos A cos B - sin A sin B, find the value of cos75°.

    
    1. A.Option 1
    2. B.Option 2
    3. C.Option 3
    4. D.Option 4
    Show answer

    Answer: C

22. Q742023 · 17 Jul 2023 · Shift 4

    Racer A and racer B run a race of 18 km on a circular track of length 800 m. Both complete one round in 200 sec and 250 sec, respectively. After how much time from the start will the faster person meet the slower person for the last time?

    1. A.2700 sec
    2. B.4000 sec
    3. C.2250 sec
    4. D.1800 sec
    Show answer

    Answer: B

23. Q592023 · 14 Jul 2023 · Shift 1

    If sin (a + b) = 1 and cos (a - b) = , then find a.

    
    1. A.75°
    2. B.30°
    3. C.15°
    4. D.45°
    Show answer

    Answer: A

24. Q682023 · 14 Jul 2023 · Shift 1

    If cos θ = , then tan2 θ cos2 θ = ?

    
    1. A.Option 1
    2. B.Option 2
    3. C.Option 3
    4. D.Option 4
    Show answer

    Answer: B

25. Q732023 · 14 Jul 2023 · Shift 1

    If {(3 sin θ – cos θ) / (cos θ + sin θ)} = 1, then the value of cot θ is:

    1. A.3
    2. B.0
    3. C.1
    4. D.2
    Show answer

    Answer: C