Algebra · SSC CGL previous year questions

2024 120 questions

1. Q562024 · 26 Sept 2024 · Shift 2

   If $x=\sqrt{6}+2$ and $y=\sqrt{6}-2$, then what is the value of $\left(\frac{x}{y}+\frac{y}{x}\right)-3$?

   1. A.22
   2. B.35
   3. C.42
   4. D.97
   Show answer

   Answer: D

2. Q622024 · 26 Sept 2024 · Shift 2

   If 2a - b = 3 and 8a³ - b³ = 999, then find the value of 4a² - b².

   1. A.61
   2. B.65
   3. C.67
   4. D.63
   Show answer

   Answer: D

3. Q702024 · 26 Sept 2024 · Shift 2

   In ΔABC, DE || BC and 5AE = 3EC. If AB = 6.4 units, then the value of DB (in units) is:

   1. A.3.2
   2. B.5
   3. C.4
   4. D.2.4
   Show answer

   Answer: C

4. Q582024 · 26 Sept 2024 · Shift 3

   If $\frac{x}{x^2-2x+1}=\frac{1}{3}$, then the value of $x^3+\frac{1}{x^3}$ is:

   1. A.110
   2. B.180
   3. C.160
   4. D.130
   Show answer

   Answer: A

5. Q602024 · 26 Sept 2024 · Shift 3

   Find the value of the unknowns: x + 1.5y + 2z = 5.5 x + 5y + 7z = 15 3x + 11y + 13z = 25

   1. A.x = 4, y = -3, z = 2
   2. B.x = -3, y = 2, z = 4
   3. C.x = 2, y = -3, z = 4
   4. D.x = 2, y = 4, z = -3
   Show answer

   Answer: C

6. Q632024 · 26 Sept 2024 · Shift 3

   If $x=a\sec \theta \cos \varphi$, $y=b\sec \theta \sin \varphi$ and $z=c\tan \theta$, then the value of $\left(\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}\right)$ is equal to:

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

   Answer: C

7. Q642024 · 26 Sept 2024 · Shift 3

   If $\cot \theta =\sqrt{11}$, then the value of $\frac{{\mathrm{cosec}}^2\theta -{\sec }^2\theta }{{\mathrm{cosec}}^2\theta +{\sec }^2\theta }$ is:

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

   Answer: B

8. Q702024 · 26 Sept 2024 · Shift 3

   The greatest value of ${\sin }^4\theta +{\cos }^4\theta$ is:

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

   Answer: A

9. Q602024 · 25 Sept 2024 · Shift 1

   The side BC of △ABC is produced to a point D. If AC = BC and ∠BAC = 70°, then find the value of ∠ACD - ∠ABC.

   1. A.60°
   2. B.70°
   3. C.45°
   4. D.75°
   Show answer

   Answer: B

10. Q682024 · 25 Sept 2024 · Shift 1

    If , then find the value of .

    
    1. A.-1/3
    2. B.1/6
    3. C.1/2
    4. D.-1/4
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    Answer: A

11. Q692024 · 25 Sept 2024 · Shift 1

    If $a^3+\frac{1}{a^3}=2$ (where a > 0), then the value of $a+\frac{1}{a}$ is:

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

    Answer: A

12. Q712024 · 25 Sept 2024 · Shift 1

    Find the values of 'a' and 'b' for which the system of equations $3x+y=3$ and $(a-b)x+(a+b)y=3a+b-3$ has infinite solutions.

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

    Answer: D

13. Q742024 · 25 Sept 2024 · Shift 1

    If , then find the value of .

    
    1. A.0
    2. B.5
    3. C.1
    4. D.10
    Show answer

    Answer: C

14. Q522024 · 25 Sept 2024 · Shift 2

    The relation between K1 and K2 for which the system of linear equations K1x + 3y = 8 and 4x + K2y = 16 represents coincident lines, is:

    1. A.K2 = 3K1
    2. B.K1 + K2 = 0
    3. C.K2 = K1
    4. D.K2 + 3K1 = 0
    Show answer

    Answer: A

15. Q702024 · 25 Sept 2024 · Shift 2

    If ${\cot }^2\theta -2{\cos }^2\theta =0$, $(0^{\circ }<\theta <90^{\circ })$, then the value of $\theta$ is:

    1. A.45°
    2. B.30°
    3. C.90°
    4. D.60°
    Show answer

    Answer: A

16. Q712024 · 25 Sept 2024 · Shift 2

    The value of $(x+y{)}^2+(x-y{)}^2$ is equal to:

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

    Answer: D

17. Q722024 · 25 Sept 2024 · Shift 2

    If $x=p\sec A\cos B$, $y=q\sec A\sin B$ and $z=r\tan A$, what is the value of the following expression? $\frac{x^2}{p^2}+\frac{y^2}{q^2}-\frac{z^2}{r^2}$

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

    Answer: D

18. Q742024 · 25 Sept 2024 · Shift 2

    Find the value of 'k' for which the system of equations 4x + 6y = 7 and 6x + (k+4)y – 21 = 0 has a unique solution.

    1. A.k ≠ 5
    2. B.k ≠ 7
    3. C.k = 5
    4. D.k = 7
    Show answer

    Answer: A

19. Q512024 · 25 Sept 2024 · Shift 3

    Find the value of $3\sin 15^{\circ }-4{\sin }^{3}15^{\circ }$.

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

    Answer: B

20. Q562024 · 25 Sept 2024 · Shift 3

    If $a^2+b^2=148$ and $ab=54$, then find the value of $\frac{a+b}{a-b}$.

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

    Answer: D

21. Q602024 · 25 Sept 2024 · Shift 3

    The value of N in the equation 9 × N of 4 ÷ 4 - 15 × 4 = 12 is:

    1. A.0
    2. B.9
    3. C.8
    4. D.12
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    Answer: C

22. Q632024 · 25 Sept 2024 · Shift 3

    What is the value of $\left(\frac{5}{\sqrt{3}}-\mathrm{cosec}60^{\circ }\right)$?

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

    Answer: D

23. Q712024 · 25 Sept 2024 · Shift 3

    If $x^2+1=x$, then the value of $(x^{14}+x^8+1)$ is:

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

    Answer: B

24. Q512024 · 24 Sept 2024 · Shift 1

    Find the greatest value of ‘k’ in a 6-digit number 6745k2 such that the number is divisible by 3.

    1. A.7
    2. B.8
    3. C.6
    4. D.9
    Show answer

    Answer: D

25. Q552024 · 24 Sept 2024 · Shift 1

    What conclusion can be drawn about the solution of the following system of linear equations in two variables: 3x + 2y = 7 2x + 3y = 7

    1. A.More than two solution
    2. B.Infinite solutions
    3. C.Unique solution
    4. D.No solution
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    Answer: C