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 $\sec\theta +\tan\theta = 3$, then what is the value of $\sec \theta-\tan \theta$?

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

Option 2: $6$

Option 3: $\frac{1}{6}$

Option 4: $\frac{1}{5}$

Question : The value of $3\frac{1}{2} - [2\frac{1}{4}+ 1\frac{1}{4} - \frac{1}{2}(1\frac{1}{2}-\frac{1}{3} -\frac{1}{6})]$ is:

Option 1: $\frac{1}{2}$

Option 2: $2\frac{1}{2}$

Option 3: $3\frac{1}{2}$

Option 4: $9\frac{1}{2}$

Question : What is the value of $\frac{\frac{5}{6} \text { of } \frac{1}{3} \times \frac{12}{25}-\frac{1}{3} \text { of } \frac{5}{6} \times \frac{18}{25}}{\frac{25}{12} \text { of } \frac{1}{6} \times \frac{2}{5}+\frac{3}{8} \text { of } \frac{12}{25} \times \frac{5}{6}}$?

Option 1: $-\frac{3}{13}$

Option 2: $-\frac{5}{13}$

Option 3: $-\frac{8}{25}$

Option 4: $-\frac{3}{25}$

Question : The value of exponential form of $\sqrt{\sqrt{2}\sqrt{3}}$ is:

Option 1: $6$

Option 2: $6^{\frac{1}{2}}$

Option 3: $6^{-\frac{1}{2}}$

Option 4: $6^{\frac{1}{4}}$