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 $a+\frac{1}{a}=2$ and $b+\frac{1}{b}=-2$, then what is the value of $a^2+\frac{1}{a^2}+b^2+\frac{1}{b^2} ?$

Option 1: 0

Option 2: 2

Option 3: 8

Option 4: 4

Question : The value of $\frac{3+8 \times 8 \div 8 \text { of } 8+7 \div 7 \times 2}{5 \div 5 \text { of } 4+3 \times 3 \div 3-3+2}$ is:

Option 1: $1 \frac{3}{5}$

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

Option 3: $1 \frac{4}{7}$

Option 4: $2 \frac{3}{7}$

Question : What is the value of $\frac{4}{3}\left(\sin ^2 35^{\circ}+\sin ^2 55^{\circ}\right) ?$

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

Option 2: $\frac{4}{3}$

Option 3: $\frac{8}{9}$

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

Question : If $a^2+\frac{1}{a^2}=\frac{7}{3}$, then what is the value of $\left(a^3-\frac{1}{a^3}\right)?$

Option 1: $\frac{5}{3 \sqrt{3}}$

Option 2: $\frac{10}{3 \sqrt{3}}$

Option 3: $\frac{7}{3 \sqrt{3}}$

Option 4: $\frac{8}{3 \sqrt{3}}$