Question : If $6x^{2}-12x+1=0$, then the value of $27x^{3}+\frac{1}{8x^{3}}$ is:

Option 1: 162

Option 2: 189

Option 3: 207

Option 4: 225

Question : If $x = \sqrt[3]{5} + 2$, then the value of $x^3-6x^2+12x-13$ is:

Option 1: $–1$

Option 2: $1$

Option 3: $2$

Option 4: $0$

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 $\frac{5x}{2}-\frac{[7(6x-\frac{3}{2})]}{4}=\frac{5}{8}$, then what is the value of $x$?

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

Option 2: $-\frac{1}{4}$

Option 3: $4$

Option 4: $–4$

Question : If $2x+\frac{1}{3x}$ = 5, then the value of $\frac{5x}{6x^{2}+20x+1}$ is:

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

Option 2: $\frac{1}{6}$

Option 3: $\frac{1}{5}$

Option 4: $\frac{1}{7}$

Question : If $x+y+z=0$, then what is the value of $\frac{x^2}{yz}+\frac{y^2}{xz}+\frac{z^2}{xy}$?

Option 1: $0$

Option 2: $\frac{1}{3}$

Option 3: $1$

Option 4: $3$