51)

If x² + 1 – 2x = 0, x > 0, then x² (x² - 2) = ________.

SSC CHSL 2021

A)

\(\sqrt 2\)

B)

1

C)

0

D)

–1

52)

If \(x^2 – 3\sqrt2x+ 1 = 0,\) then what is the value of \({x^3} + \left( {\frac{1}{{{x^3}}}} \right)\)?

SSC CHSL 2021

A)

\(30\sqrt 2\)

B)

\(30\sqrt 6\)

C)

\(45\sqrt 2\)

D)

\(15\sqrt 6\)

53)

The coefficient of x³ y in (x - 2y) × (5x + y)³ is:

SSC CHSL 2021

A)

75

B)

-175

C)

250

D)

-150

54)

The value of \({5\over4}\times2{2\over3}\div{5\over9}\)\(of\space 1{1\over5}+{2\over25}\times\)\(4{1\over6}\div{2\over7}\)\(of\space2 \frac{1}{3}\) is:

SSC CHSL 2021

A)

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

B)

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

C)

\(5\frac{1}{2}\)

D)

\(3\frac{1}{2}\)

55)

If x + y + z = 13, x² + y² + z² = 91 and xz = y², then the difference between z and x is:

SSC CHSL 2021

A)

5

B)

9

C)

8

D)

3

56)

If x² + 4y² + 3z² +\(\frac{19}{4}=2\sqrt{3}\)\((x+y+z)\) , then the value of (x - 4y + 3z) is:

SSC CHSL 2021

A)

\(\frac{\sqrt{3}}{2}\)

B)

\(2\sqrt{3}\)

C)

\(\sqrt{3}\)

D)

\(\frac{\sqrt{3}}{3}\)

57)

If (4X - 5)³ + (X - 2)³ + 27(2X - 5)³ = 9(4X - 5)(X - 2)(2X - 5), then the value of \(\left(x+\frac{3}{2}\right)\) will be:

SSC CHSL 2021

A)

\(\frac{3}{2}\)

B)

\(\frac{5}{2}\)

C)

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

D)

\(\frac{7}{2}\)

58)

If 9a² + 4b² + 49c² + 18 = 2(2b + 28c - 3a), then the value of (a + 2b - c) will be:

SSC CHSL 2021

A)

\(\frac{2}{21}\)

B)

\(\frac{26}{21}\)

C)

\(\frac{11}{21}\)

D)

\(\frac{5}{21}\)

59)

If 9x² - 6x + 1 = 0, then the value of 27x³ + (27x³)^-1 will be:

SSC CHSL 2021

A)

2

B)

4

C)

1

D)

8

60)

If a + b = 24 and a² + b² = 306, where a > b, then the value of 4a - 5b is:

SSC CHSL 2021

A)

12

B)

18

C)

20

D)

15