251)

If x + y = 36, then find (x - 27)³ + (y - 9)³.

SSC CGL 2022

A)

2y

B)

81

C)

1

D)

0

252)

If \(y + {1 \over y} = 3\)\(\), then what is the value of \({{1} \over y^3} + y^3 + 2\)?

SSC CGL 2022

A)

20

B)

18

C)

24

D)

29

253)

If \({{a^2 + b^2 + c^2 - 1024} \over ab - bc - ca} = -2\) and a + b = 5c, where c > 0, then the value of c is ________________.

SSC CGL 2022

A)

12

B)

4

C)

8

D)

5

254)

If P + Q = 6 and PQ  = 4, then what is the value of P³ + Q³?

SSC CGL 2022

A)

144

B)

64

C)

81

D)

256

255)

If \(x = 2 - 2^\frac{1}{3} + 2^\frac{2}{3}\) , then find the value of x³ - 6x² + 18x.

SSC CGL 2022

A)

45

B)

33

C)

40

D)

22

256)

If a + b + c = 5, a + b³ + c³ = 85 and abc = 25, then find the value of a² + b²+ c² - ab - bc - ca.

SSC CGL 2022

A)

6

B)

4

C)

2

D)

8

257)

If a = -12, b = -6 and c = 18, then what is the value of (2abc)/9

SSC CGL 2022

A)

-288

B)

288

C)

554

D)

144

258)

If, \(\frac{r}{13} + \frac{13}{r} = 1\) then the value of r³ is:

SSC CGL 2022

A)

2157

B)

2197

C)

-2157

D)

-2197

259)

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

SSC CGL 2022

A)

1

B)

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

C)

zero

D)

- 1

260)

Which of the following statement is correct?
I. The value of 100² - 99² + 98² -97²+96²-95²+94²-93²+.......+22²-21² is 4840.
II. The value of \((k^{2}+ \frac{1}{k^{2}})(k - \frac{1}{k})(k^{4} + \frac{1}{k^{4}})(k + \frac{1}{k})(k^{4} - \frac{1}{k^{4}})\) is \(k^{16}- \frac{1}{k^{16}}\).

SSC CGL 2022

A)

Only II

B)

Both I and II

C)

Neither I nor II

D)

Only I