271)

If \({a} + \frac{1}{{{a}}}=5\) , then what is the value of \({a^3} + \frac{1}{{{a^3}}}\)?

SSC CGL 2022

A)

105

B)

15

C)

110

D)

–10

272)

What is the value of a² + b² + c² - 2ab - 2bc + 2ca ?

SSC CGL 2022

A)

(a – b – 2c)²

B)

(a – b + c)²

C)

(2a + b + c)²

D)

(a + 2b – c)²

273)

If \(\frac{x}{8} + \frac{8}{x} = 1\) , then the value of x³ is :

SSC CGL 2022

A)

256

B)

-512

C)

-256

D)

512

274)

If p = 8.15, q = 9.06 and r = -17.21, then the value of p³ + q³ + r³ - 3pqr is:

SSC CGL 2022

A)

4.75

B)

-5.62

C)

-3.81

D)

0

275)

If \(x^4 + \frac{16}{x^4} \)= 15617, x > 0, then find the value of \(x + \frac{2}{x} \) .

SSC CGL 2022

A)

\(\sqrt{123}\)

B)

\(\sqrt{129}\)

C)

\(\sqrt{121}\)

D)

\(\sqrt{127}\)

276)

If x = 222, y = 223 and z = 224, then find the value of x³ + y³ + z³ - 3xyz.

SSC CGL 2022

A)

2006

B)

2004

C)

2007

D)

2005

277)

If α, β are the roots of \(6x^2 + 13x + 7 = 0\), then the equation whose roots are \(α^2, β^2\) is:

SSC CGL 2022

A)

\(36x^2\) - \(85x\) - 49 = 0

B)

\(36x^2\) - \(85x\) + 49 = 0

C)

\(36x^2\) - \(87x \)+ 49 = 0

D)

\(36x^2\) + \(87x\) - 49 = 0

278)

If x + y + z = 0 and x² + y² + z² = 40, then what is the value of xy + yz + zx?

SSC CGL 2022

A)

-5

B)

5

C)

-20

D)

-10