Question : If $2x + {\frac{2}{9x}} = 4$, then the value of $27x^3 + \frac{1}{27x^{3}}$ is:

Option 1: 180

Option 2: 198

Option 3: 234

Option 4: 252

Question : If $x+ \frac{1}{9x}=4$, then the value of $9x^2+ \frac{1}{9x^2}$ is:

Option 1: 140

Option 2: 142

Option 3: 144

Option 4: 146

Question : If $2x-\frac{1}{2x}=5,x\neq0$, then the value of $(x^2+\frac{1}{16x^2}-2)$is:

Option 1: $\frac{19}{4}$

Option 2: $\frac{23}{4}$

Option 3: $\frac{27}{4}$

Option 4: $\frac{31}{4}$

Question : When $2x+\frac{2}{x}=3$, then the value of ($x^3+\frac{1}{x^3}+2)$ is:

Option 1: $\frac{2}{7}$

Option 2: $\frac{7}{8}$

Option 3: $\frac{7}{2}$

Option 4: $\frac{8}{7}$

Question : If $2x+\frac{2}{x}=3$, then the value of $x^{3}+\frac{1}{x^{3}}+2$ is:

Option 1: $\frac{3}{4}$

Option 2: $\frac{4}{5}$

Option 3: $\frac{5}{8}$

Option 4: $\frac{7}{8}$

Question : If $\frac{3}{(x+2)(2x+1)}=\frac{a}{2x+1}+\frac{b}{x+2}$ is an identity, the value of $b$ is:

Option 1: 0

Option 2: –1

Option 3: 2

Option 4: 3