Question : If $\mathrm{K}+\frac{1}{\mathrm{~K}}+2=0$ and $\mathrm{K}<0$, then what is the value of $\mathrm{K}^{11}+\frac{1}{\mathrm{~K}^4}$?

Option 1: 0

Option 2: –2

Option 3: –1

Option 4: –17

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

Option 1: 410

Option 2: 192

Option 3: 212

Option 4: 194

Question : What is the value of
$
\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)\left(\mathrm{k}^8+\frac{1}{\mathrm{k}^8}\right)\left(\mathrm{k}^{16}+\frac{1}{\mathrm{k}^{16}}\right)\left(\mathrm{k}^{32}+\frac{1}{\mathrm{k}^{32}}\right)?
$

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

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

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

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

Question : If $x+\frac{1}{x}=-2$, then what is the value of $x^{17}+x^{-17}+x^{12}+x^{-12} ?(x<0)$

Option 1: –2

Option 2: –1

Option 3: 1

Option 4: 0

Question : Which of the following is correct?

Option 1: $\frac{2}{3}< \frac{3}{5}< \frac{11}{15}$

Option 2: $\frac{3}{5}< \frac{2}{3}< \frac{11}{15}$

Option 3: $\frac{11}{15}< \frac{3}{5}< \frac{2}{3}$

Option 4: $\frac{3}{5}< \frac{11}{15}< \frac{2}{3}$