211)

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

212)

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

213)

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

214)

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

215)

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

216)

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

217)

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)

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

218)

If 8k⁶ + 15k³ – 2 = 0, then the positive value of \(\left( {{\rm{k}}\,{\rm{ + }}\,\frac{1}{{\rm{k}}}} \right)\) is :

SSC CGL 2022

A)

\(8\frac{1}{2}\)

B)

\(2\frac{1}{8}\)

C)

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

D)

\(8\frac{1}{8}\)

219)

What is the value of x, if \(5\left( {1 - \frac{x}{5}} \right) - (5 - x) - \frac{1}{{200}}{\rm{of (20 - x) = 0}}{\rm{.08}}\) ?

SSC CGL 2022

A)

24

B)

9

C)

18

D)

36

220)

If x + y + z = 18, xyz = 81 and xy + yz + zx = 90, then the value of x³ + y³ + z³ + xyz is :

SSC CGL 2022

A)

1225

B)

1250

C)

1321

D)

1296