Question : If $x + 3y = 6$, what is the value of $x^3 + 27y^3 + 54 xy$?

Option 1: 264

Option 2: 258

Option 3: 216

Option 4: 220

Question : If $2x+3y = 4$ and $4x^{2}+9y^{2}= 64$, then what is the value of $8x^{3}+27y^{3}$:

Option 1: 253

Option 2: 235

Option 3: 352

Option 4: 325

Question : If $x=(\sqrt{6}-1)^{\frac{1}{3}}$, then the value of $\left(x-\frac{1}{x}\right)^3+3\left(x-\frac{1}{x}\right)$ is:

Option 1: $\frac{2 \sqrt{6}-6}{5}$

Option 2: $\frac{4 \sqrt{6}-6}{5}$

Option 3: $\frac{4 \sqrt{6}-6}{3}$

Option 4: $\frac{4 \sqrt{3}-6}{5}$

Question : If $x=3+2\sqrt{2}$, then $\frac{x^{6}+x^{4}+x^{2}+1}{x^{3}}$ is equal to:

Option 1: 216

Option 2: 192

Option 3: 198

Option 4: 204

Question : If $\left(x-\frac{1}{x}\right) =4$, then what is the value of $\left(x^6+\frac{1}{x^6}\right)$?

Option 1: 4689

Option 2: 4786

Option 3: 5832

Option 4: 5778

Question : If $6^{x}=3^{y}=2^{z}$, then what is the value of $\frac{1}{y}+\frac{1}{z}-\frac{1}{x}$?

Option 1: 1

Option 2: 0

Option 3: 3

Option 4: 6