Question : If $\left(w+\frac{1}{w}\right)=6$, then what will be the value of $\left(w-\frac{1}{w}\right)?$

Option 1: $4 \sqrt{2}$

Option 2: $\sqrt{2}$

Option 3: $3 \sqrt{2}$

Option 4: $2 \sqrt{2}$

Question : If $A=30^{\circ}$, then find the value of $\frac{(2 \tan A)}{\left(1-\tan^2 A\right)}$.

Option 1: $4 \sqrt{3}$

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

Option 3: $3$

Option 4: $2 \sqrt{3}$

Question : If $x=5–\sqrt{21}$, the value of $\frac{\sqrt{x}}{\sqrt{32–2x}–\sqrt{21}}$ is:

Option 1: $\frac{1}{\sqrt2}(\sqrt{3}–\sqrt{7})$

Option 2: $\frac{1}{\sqrt2}(\sqrt{7}–\sqrt{3})$

Option 3: $\frac{1}{\sqrt2}(\sqrt{7}+\sqrt{3})$

Option 4: $\frac{1}{\sqrt2}(7–\sqrt{3})$

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 $K+\frac{1}{K}=-3$, then what is the value of $\left(\frac{K^6+1}{K^3}\right)+\left(\frac{K^4+1}{K^2}\right)$?

Option 1: 27

Option 2: – 29

Option 3: 29

Option 4: – 27