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

Option 1: $16 {K}^4-16 {K}^2-1$

Option 2: $8 {K}^4+4 {K}^2-1$

Option 3: $16 {K}^4-16 {K}^2+2$

Option 4: $16 {K}^4-4 {K}^2-1$

Question : If $\sqrt{\frac{\mathrm{a}}{\mathrm{b}}}=\frac{8}{3}-\sqrt{\frac{\mathrm{b}}{\mathrm{a}}}$ and $a-b=10$, then the value of $ab$ is:

Option 1: $32 \frac{1}{7}$

Option 2: $32 \frac{3}{7}$

Option 3: $32 \frac{4}{7}$

Option 4: $32 \frac{2}{7}$

Question : What is the value of $\left(k-\frac{1}{k}\right)\left(k^2+\frac{1}{k^2}\right)\left(k^4+\frac{1}{k^4}\right)\left(k^8+\frac{1}{k^8}\right)\left(k^{16}+\frac{1}{k^{16}}\right) ?$

Option 1: $k^{64}-\frac{1}{k^{64}}$

Option 2: $\frac{k^{32}-\frac{1}{k^{32}}}{k-\frac{1}{k}}$

Option 3: $k^{32}-\frac{1}{k^{32}}$

Option 4: $\frac{k^{32}-\frac{1}{k^{32}}}{k+\frac{1}{k}}$

Question : What is the value of $\frac{1+\mathrm{x}}{1-\mathrm{x}^2} \div \frac{1+\mathrm{x}}{1-\mathrm{x}^4}-\frac{1-\mathrm{x}^4}{1-\mathrm{x}} \times \frac{1+\mathrm{x}}{1-\mathrm{x}^2}$?

Option 1: $\frac{2 \mathrm{x}\left(1+\mathrm{x}^2\right)}{(1-\mathrm{x})}$

Option 2: $\frac{2 \mathrm{x}\left(1+\mathrm{x}^2\right)}{(\mathrm{x}-1)}$

Option 3: $(1-\mathrm{x})^2$

Option 4: $\left(1+\mathrm{x}^2\right)$