21)

\(\sqrt{x}-{1\over \sqrt{x}}= \sqrt{3}\), then what is the value of  \(x^4+\frac{1}{{{x^4}}} \)?

SSC CGL 2022

A)

623

B)

7

C)

531

D)

527

22)

If a³ + b³ = 218 and a + b = 2, then the value of \(\sqrt {1 - ab}\) is:

SSC CGL 2022

A)

5

B)

3

C)

4

D)

6

23)

If x + y + z = 7, xy + yz + zx = 8, then what is the value of x³ + y³ + z³ - 3xyz?

SSC CGL 2022

A)

125

B)

150

C)

175

D)

200

24)

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

SSC CGL 2022

A)

-4

B)

-3

C)

5

D)

1

25)

If x² - 5x - 1 = 0, what is the value of
\( \frac{{{x^6} - {x^4} + {x^2} - 1}}{{{x^3}}}\) ?

SSC CGL 2022

A)

130

B)

140

C)

145

D)

135

26)

If a + b + c = 11 and ab + bc + ca = 28, then find the value of a³ + b³ + c³ - 3abc.

SSC CGL 2022

A)

1639

B)

407

C)

1093

D)

2255

27)

If (x + y)³ - (x - y)³ - 3y(2x² - 3y²) = ky³, then find the value of k.

SSC CGL 2022

A)

10

B)

11

C)

8

D)

10.5

28)

If \(x^2+\frac{1}{x^2}=18, x>0\) then find the value of \(x^3+\frac{1}{x^3}\),

SSC CGL 2022

A)

52

B)

\(34 \sqrt{5}\)

C)

\(46 \sqrt{5}\)

D)

\(17 \sqrt{5}\)

29)

If\( \sqrt{x}-{1 \over \sqrt{x}} = \sqrt{5}\) , x ≠ 0, then what is the value of \((x^4+{1\over{x^2}})\over(x^2+1)\)?

SSC CGL 2022

A)

42

B)

46

C)

48

D)

44

30)

If 6√ 6 p³ +2√ 2 q³ = (√ 6p + √ 2q)(Sp² + Mq² - Npq), then the positive value of \(\sqrt{S^2+M^2+2N^2}\) is:

SSC CGL 2022

A)

9

B)

10

C)

8

D)

12