Algebra · SSC CGL previous year questions

2024 120 questions

1. Q712024 · 19 Sept 2024 · Shift 2

   The maximum value of $(2\sin \theta +3\cos \theta )$ is:

   1. A.9
   2. B.√17
   3. C.√11
   4. D.√13
   Show answer

   Answer: D

2. Q522024 · 19 Sept 2024 · Shift 3

   The value of $[15÷3\times 7-8\text{ of }2+6]$ is:

   1. A.25
   2. B.−29
   3. C.39.5
   4. D.13
   Show answer

   Answer: A

3. Q612024 · 19 Sept 2024 · Shift 3

   If , then find the value of:

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

   Answer: D

4. Q722024 · 19 Sept 2024 · Shift 3

   For the equations $ax+(a^2+1)y=4$ and $4x+ay=a^2$, which of the following statements is TRUE?

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

   Answer: B

5. Q582024 · 18 Sept 2024 · Shift 1

   If , then find the value of .

   
   1. A.188
   2. B.194
   3. C.186
   4. D.196
   Show answer

   Answer: B

6. Q622024 · 18 Sept 2024 · Shift 1

   If $3\sin A+4\cos A=5$, then the value of $\tan A$ is:

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

   Answer: B

7. Q542024 · 18 Sept 2024 · Shift 2

   If , then find the value of .

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

   Answer: D

8. Q552024 · 18 Sept 2024 · Shift 2

   Find the value of $\frac{\tan 55^{\circ }}{\cot 35^{\circ }}$.

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

   Answer: A

9. Q642024 · 18 Sept 2024 · Shift 3

   The value of 9 - 5 × 6 + {29 - (7 - 2)} ÷ 8 is:

   1. A.-18
   2. B.18
   3. C.-8
   4. D.8
   Show answer

   Answer: A

10. Q682024 · 18 Sept 2024 · Shift 3

    If the 9-digit number 5x79856y6 is divisible by 36, then what is the negative value of √(2x + y) for the largest possible value of y, given x and y are natural numbers?

    1. A.-5
    2. B.-4
    3. C.-2
    4. D.-7
    Show answer

    Answer: A

11. Q722024 · 18 Sept 2024 · Shift 3

    What is the value of $\sqrt{\frac{9{\sin }^{2}26^{\circ }+9{\sin }^{2}64^{\circ }+36}{32-7{\cos }^{2}32^{\circ }-7{\cos }^{2}58^{\circ }}}$?

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

    Answer: C

12. Q512024 · 17 Sept 2024 · Shift 1

    If $\cos 24^{\circ }=\frac{m}{n}$, then the value of $(\mathrm{cosec}24^{\circ }-\cos 66^{\circ })$ is:

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

    Answer: C

13. Q652024 · 17 Sept 2024 · Shift 1

    For what value of k, the system of equations kx - 15y + 7 = 0 and 7x - 21y - 19 = 0 has NO solution?

    1. A.12
    2. B.25
    3. C.5
    4. D.6
    Show answer

    Answer: C

14. Q702024 · 17 Sept 2024 · Shift 1

    Find the least value of k for which a 7-digit number 249k876 is divisible by 6.

    1. A.5
    2. B.0
    3. C.7
    4. D.1
    Show answer

    Answer: B

15. Q712024 · 17 Sept 2024 · Shift 1

    If $\sec \theta =\frac{29}{20}$ where $0<\theta <90^{\circ }$, then what is the value of $3\mathrm{cosec}\theta +3\cot \theta$?

    1. A.7
    2. B.49
    3. C.14
    4. D.7/3 cosec
    Show answer

    Answer: A

16. Q512024 · 17 Sept 2024 · Shift 2

    Find the least value of x for which 57x716 is divisible by 9.

    1. A.8
    2. B.9
    3. C.0
    4. D.1
    Show answer

    Answer: D

17. Q532024 · 17 Sept 2024 · Shift 2

    For what value of k, the system of equations 4x + 12y + 36 = 0 and 5x + ky + 45 = 0 has an infinite number of solutions?

    1. A.22
    2. B.20
    3. C.25
    4. D.15
    Show answer

    Answer: D

18. Q652024 · 17 Sept 2024 · Shift 2

    If , then find the value of .

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

    Answer: B

19. Q672024 · 17 Sept 2024 · Shift 2

    Find the value of $\left[\frac{4\cos (90-\theta ){\sin }^2(90+\theta )-4\sin (90+\theta ){\cos }^2(90-\theta )}{\cos \left(\frac{180+8\theta }{2}\right)}\right]$.

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

    Answer: A

20. Q692024 · 17 Sept 2024 · Shift 2

    If $a^3+3a^2+3a=7$, then the value of $a^2+2a$ is:

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

    Answer: C

21. Q532024 · 17 Sept 2024 · Shift 3

    If x is an integer such that , then find the value of .

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

    Answer: C

22. Q632024 · 17 Sept 2024 · Shift 3

    If $\sin \theta +\cos \theta =\sqrt{3}\cos \theta$, then the value of $\cot \theta$ is:

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

    Answer: C

23. Q712024 · 17 Sept 2024 · Shift 3

    If $\mathrm{cosec}x=\frac{5}{4}$, then the value of $\frac{5{\sin }^{2}x+8{\cot }^{2}x}{27{\tan }^{2}x-125{\cos }^{2}x}$ is:

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

    Answer: C

24. Q582024 · 13 Sept 2024 · Shift 1

    If $\sin 31^{\circ }=\alpha$, then the value of $\cot 59^{\circ }$ is:

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

    Answer: A

25. Q592024 · 13 Sept 2024 · Shift 1

    If $\frac{1}{1-\sin \theta }+\frac{1}{1+\sin \theta }=4\sec \theta$, $(0<\theta <90^{\circ })$, then the value of $(\cot \theta +\mathrm{cosec}\theta )$ is:

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

    Answer: D