Question : Find the value of the given expression:
$\frac{(4\frac{1}{3}+3\frac{1}{3}\times 1\frac{4}{5}\div 3\frac{3}{4}\times (1\frac{1}{2}+1\frac{1}{3}))}{(\frac{2}{3}\div \frac{5}{6}\times \frac{2}{3})}$

Option 1: $11 \frac{3}{8}$

Option 2: $10\frac{1}{8}$

Option 3: $14\frac{3}{8}$

Option 4: $16\frac{5}{8}$

Question : If $X$ is 20% less than $Y$, then find the values of$\frac{Y–X}{Y}$ and $\frac{X}{X–Y}$.

Option 1: $\frac{1}{5}$ and $-4$

Option 2: $5$ and $-\frac{1}{4}$

Option 3: $\frac{2}{5}$ and $-\frac{5}{2}$

Option 4: $\frac{3}{5}$ and $-\frac{5}{3}$

Question : Simplify the expression:
$\frac{1}{8}\left[\frac{1}{b-1}-\frac{1}{b+1}-\frac{2}{b^2+1}-\frac{4}{b^4+1}\right]$

Option 1: $\frac{1}{b^8-1}$

Option 2: $\frac{8}{b^8+1}$

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

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

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 : If $x=(7+3 \sqrt{5})$, then find the value of $x^2+\frac{1}{x^2}$.

Option 1: $ \frac{580+315 \sqrt{5}}{8}$

Option 2: $\frac{799+328 \sqrt{5}}{8}$

Option 3: $\frac{799+315 \sqrt{5}}{12}$

Option 4: $\frac{799+315 \sqrt{5}}{8}$