81)

Simplify the given expression.
\(\left(x-\frac{2}{x}\right)^3-\left(x+\frac{2}{x}\right)^3\)

SSC CHSL 2021

A)

\(-4\left(x^3+\frac{4}{x^3}\right)\)

B)

\(-4\left(3x+\frac{4}{x^3}\right)\)

C)

\(2\left(x-\frac{4}{x^3}\right)\)

D)

\(4\left(3x-\frac{4}{x^3}\right)\)

82)

If \(x+{1\over15x}=3\), then the value of \(9x^3+\frac{1}{375x^3}\) will be:

SSC CHSL 2021

A)

237.6

B)

376.2

C)

273.6

D)

367.2

83)

If x⁶ - 6√6y⁶ = (x² + Ay²)(x⁴ + Bx²y² + Cy⁴), then what will be the value of (A² - B² + C²)?

SSC CHSL 2021

A)

18

B)

36

C)

27

D)

42

84)

If 2x + 3y + 4z = 11, 8x³ + 27y³ + 64z³ = 105 and xyz = 1, then the value 4x² + 9y² + 16z² - 6xy - 12yz - 8xz is:

SSC CHSL 2021

A)

3

B)

4

C)

6

D)

5

85)

If \(x+{1\over3x}=5\), then the value of \(27x^3+\frac{1}{x^3}\) will be:

SSC CHSL 2021

A)

3024

B)

3042

C)

3240

D)

3420

86)

If 1 + 4x² + 16x⁴ = 512 and 1 - 2x + 4x² = 64, then the value of 1 + 2x + 4x² is:

SSC CHSL 2021

A)

10

B)

8

C)

6

D)

12

87)

If a + b + c = 11 and ab + bc + ca = 15, then what is the value of a³ + b³ + c³ - 3abc?

SSC CHSL 2021

A)

836

B)

386

C)

638

D)

368

88)

If a + b + c = 5, a² + b² + c² = 27, a³ + b³ + c³ = 125, then the value of \(\frac{abc}{5}\) is :

SSC CHSL 2021

A)

5

B)

-5

C)

1

D)

-1

89)

If (x - 1.5)³ + (x - 4)³ + (x - 3.5)³ = 3(x - 1.5)(x - 4)(x - 3.5), then what is the value of x?

SSC CHSL 2021

A)

1

B)

6

C)

3

D)

9

90)

If 3x + 5y = 14 and xy = 6, then what is the value of 9x² + 25y² ?

SSC CHSL 2021

A)

20

B)

14

C)

182

D)

16