1)

If (x + 6y) = 8, and xy = 2, where x > 0, what is the value of (x³ + 216y³)?

SSC CGL 2022

A)

476

B)

368

C)

224

D)

288

2)

If x + y + 3 = 0, then find the value of x³ + y³ - 9xy + 9.

SSC CGL 2022

A)

-36

B)

-18

C)

36

D)

18

3)

Simplify the following expression: \({{{(a^2-4b^2)}^3} + 64 {{(b^2 - 4c^2)}^3} + {{(16c^2 -a^2})^3}} \over {{(a-2b)^3} +{(2b-4c)^3} +{(4c-a)^3}}\)

SSC CGL 2022

A)

4(a + 2b) (b + 2c) (4c + a)

B)

2(a + 2b) (b + 2c) (4c + a)

C)

-(a + 2b) (b +2c) (4c + a)

D)

(a + 2b) (b + 2c) (4c + a)

4)

If (4x+2y)³+(4x−2y)³=16(Ax³+Bxy²), then what is the value of \({1\over 2 }{(\sqrt{A^2 +B^2})}\)?

SSC CGL 2022

A)

8

B)

5

C)

3

D)

7

5)

If \(x = 4 + \sqrt{15}\) , what is the value of \( \left( {{x^2}\, + \,\frac{1}{{{x^2}}}} \right)\)?

SSC CGL 2022

A)

72

B)

48

C)

54

D)

62

6)

If a² + b² + c² = 6.25 and (ab + bc + ca) = 0.52, what is the value of (a + b + c), if (a + b + c) < 0?

SSC CGL 2022

A)

-2.7

B)

±2.7

C)

±2.8

D)

-2.8

7)

If x + y + z = 11, xy + yz + zx = -6, and x³ + y³ + z³ = 1604, then the value of xyz is:

SSC CGL 2022

A)

1

B)

4

C)

5

D)

25

8)

If a² + b² + 49c² + 18 = 2(b - 28c - a) then the value of (a + b - 7c) is:

SSC CGL 2022

A)

2

B)

3

C)

4

D)

1

9)

If a + b + c = 6, a² + b² + c² = 32, and a³ + b³ + c³ = 189, then the value of abc - 3 is:

SSC CGL 2022

A)

1

B)

3

C)

2

D)

0

10)

If x - y + z = 0, then find the value of \(\frac{{{y^2}}}{{2xz}}\, - \,\frac{{{x^2}}}{{2yz}}\, - \,\frac{{{z^2}}}{{2xy}} \)

SSC CGL 2022

A)

-6

B)

\(\frac{1}{2}\)

C)

\(\frac{3}{2}\)

D)

\(- \frac{3}{2}\)