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 $x=(\sqrt{6}-1)^{\frac{1}{3}}$, 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 $x=\sqrt{3}-\frac{1}{\sqrt{3}}, y=\sqrt{3}+\frac{1}{\sqrt{3}}$, then the value of $\frac{x^2}{y}+\frac{y^2}{x}$ is:

Option 1: $\sqrt{3}$

Option 2: $3\sqrt{3}$

Option 3: $16\sqrt{3}$

Option 4: $2\sqrt{3}$

Question : If $x+\frac{1}{x}=\sqrt{3}$ then, the value of $x^{30}+x^{24}+x^{18}+x^{12}+x^{6}+1$ is:

Option 1: $\sqrt{3}$

Option 2: $-\sqrt{3}$

Option 3: $1$

Option 4: $0$

Question : If $x=\sqrt3+\frac{1}{\sqrt3}$, then the value of $(x-\frac{\sqrt{126}}{\sqrt{42}})(x-\frac{1}{x-\frac{2\sqrt3}{3}})$ is:

Option 1: $\frac{5\sqrt3}{6}$

Option 2: $\frac{2\sqrt3}{3}$

Option 3: $\frac{5}{6}$

Option 4: $\frac{2}{3}$

Question : If $x^{4}+\frac{1}{x^{4}}=16$, then what is the value of $x^{2}+\frac{1}{x^{2}}$?

Option 1: $3 \sqrt{2}$

Option 2: $2 \sqrt{2}$

Option 3: $5 \sqrt{2 }$

Option 4: $4 \sqrt{2}$