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

Option 1: 16

Option 2: 14

Option 3: 12

Option 4: 20

Question : If $x>1$ and $x+\frac{1}{x}=2\frac{1}{12}$, then the value of $x^{4}-\frac{1}{x^{4}}$ is:

Option 1: $\frac{58975}{20736}$

Option 2: $\frac{59825}{20736}$

Option 3: $\frac{57985}{20736}$

Option 4: $\frac{57895}{20736}$

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

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

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

Option 3: $\frac{5}{2}$

Option 4: $\frac{5}{3}$

Question : If $x+\frac{1}{x}=2$, then the value of $x^{11}+\frac{1}{x^{20}}$ is:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 7

Question : If $2 x+\frac{2}{x}=5$, then the value of $\left(x^3+\frac{1}{x^3}+2\right)$ will be:

Option 1: $\frac{81}{11}$

Option 2: $\frac{81}{7}$

Option 3: $\frac{71}{8}$

Option 4: $\frac{81}{8}$