31)

If x + y + z = 4, xy + yz + zx = 1 and x³ + y³ + z³ = 34 , then what is the value of 2xyz ?

SSC CHSL 2021

A)

8

B)

-12

C)

-6

D)

18

32)

If \(x+{1\over x}=7\), then \(x^3 + \dfrac{1}{x^3}\) is equal to:

SSC CHSL 2021

A)

340

B)

161

C)

343

D)

322

33)

If x² + y² = 45 and x - y = 5 then what is the value of x³ - y³?

SSC CHSL 2021

A)

-25

B)

250

C)

150

D)

275

34)

If a³ + b³ + c³ - 3abc = 250 and a + b + c = 10, then what will be the value of \(\frac{1}{5}(ab+bc+ca)\) ?

SSC CHSL 2021

A)

5

B)

25

C)

15

D)

10

35)

If x + y + z = 3, x² + y² + z² = 45 and x³ + y³ + z³ = 69 then what is the value of xyz?

SSC CHSL 2021

A)

30

B)

40

C)

-30

D)

-40

36)

If 4√3x² + 5x -2√3 = (Ax + 2)(Bx + C). then what is the value of (A + B + C)?(A>0)

SSC CHSL 2021

A)

4

B)

4 + √3

C)

4 - √3

D)

2√3

37)

If \(x+{1\over x}= \sqrt7\), then what is the value of \((x^2 + 1)\div\left[x^4+\left(\frac{1}{x^2}\right)\right]\)?

SSC CHSL 2021

A)

\(\frac{1}{4}\)

B)

2√7

C)

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

D)

3√7

38)

If \(x - y ={7\over4}\) and \(\frac{1}{x}-\frac{1}{y}=\frac{14}{3}\), then x³ - y³ is equal to:

SSC CHSL 2021

A)

\(\frac{433}{32}\)

B)

\(\frac{433}{64}\)

C)

\(\frac{217}{64}\)

D)

\(\frac{217}{32}\)

39)

If a⁴ + b⁴ + a²b² = 133 and a² + b² - ab = 19, then the value of ab will be:

SSC CHSL 2021

A)

-9

B)

-6

C)

12

D)

15

40)

If x² - 5√2x - 1 = 0, then what will be the value of \(x^3 - \frac{1}{x^3}\) ?

SSC CHSL 2021

A)

250√2

B)

255√2

C)

485√2

D)

265√2