41)

If a + b + c = 4, ab + bc + ca = -14 and abc = -18, then the value of \(\sqrt{4a^3+4b^3+4c^3-36}\) will be:

SSC CHSL 2021

A)

25

B)

24

C)

18

D)

26

42)

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

SSC CHSL 2021

A)

2

B)

6

C)

-1

D)

4

43)

If x⁸ – 2599x⁴ + 1 = 0, then the positive value of \(x-\frac{1}{x}\) will be:

SSC CHSL 2021

A)

6

B)

12

C)

7

D)

8

44)

If a + b = p, ab = q, then (a⁴ + b⁴) is equal to

SSC CHSL 2021

A)

p⁴ - 4p²q + 2q²

B)

p⁴ - 4p²q² + 2q​²

C)

p⁴- 2p²q² + q​²

D)

p⁴- 4p²q + q​²

45)

If \((x+{1\over x})^3=27\), then what is the value of \(\left( x^2 + \frac{1}{x^2} \right) \)? Given that x is real.

SSC CHSL 2021

A)

7

B)

25

C)

11

D)

9

46)

Using algebraic identities, simplify the following expression.
\(\frac{(x^4 + x^2 + 1)}{(x^2 + x + 1)}\)

SSC CHSL 2021

A)

(x² - x + 1)

B)

(x²+ x + 1)

C)

(x²- 2x + 1)

D)

(x²+ 2x + 1)

47)

If \(\sqrt x+{1\over\sqrt x}=\sqrt6\), then the value of \(x^6 + \frac{1}{x^6}\) will be:

SSC CHSL 2021

A)

2270

B)

2502

C)

2712

D)

2702

48)

If \(x^4+{1\over x^4}=3842\), then the positive value of \( x + \frac{1}{x}\) will be:

SSC CHSL 2021

A)

10

B)

8

C)

6

D)

12

49)

If \(x-{2\over x}=4\), then what will be the value of \( x^2 + \frac{4}{x^2}\)?

SSC CHSL 2021

A)

18

B)

20

C)

12

D)

8

50)

If a + b + c = 7 and a³ + b³ + c³ – 3abc = 301, then ab + bc + ca = ?

SSC CHSL 2021

A)

2

B)

–2

C)

-4

D)

3