Question : If $x+\frac{1}{x}=\mathrm{\frac{K}{2}}$, then what is the value of $\frac{x^8+1}{x^4} ?$

Option 1: $\frac{\mathrm{K}^4-16 \mathrm{~K}^2+32}{16}$

Option 2: $\frac{\mathrm{K}^4-8 \mathrm{~K}^2-36}{32}$

Option 3: $\frac{\mathrm{K}^4-8 \mathrm{~K}^2-32}{16}$

Option 4: $\frac{\mathrm{K}^4-8 \mathrm{~K}^2+32}{16}$

Question : What is the value of $\left(\mathrm{k}+\frac{1}{\mathrm{k}}\right)\left(\mathrm{k}-\frac{1}{\mathrm{k}}\right)\left(\mathrm{k}^2+\frac{1}{\mathrm{k}^2}\right)\left(\mathrm{k}^4+\frac{1}{\mathrm{k}^4}\right)$?

Option 1: $\mathrm{k}^{16}+\frac{1}{\mathrm{k}^{16}}$

Option 2: $\mathrm{k}^{16}-\frac{1}{\mathrm{k}^{16}}$

Option 3: $\mathrm{k}^8-\frac{1}{\mathrm{k}^8}$

Option 4: $\mathrm{k}^8+\frac{1}{\mathrm{k}^8}$

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 $2 x+\frac{2}{x}=5$, 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: $\frac{81}{8}$

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: $4 \sqrt{2}$