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 $\operatorname{cosec} \theta=1 \frac{7}{22}$, then find the value of $\cot ^2 \theta$.

Option 1: $\frac{49}{484}$

Option 2: $\frac{357}{484}$

Option 3: $\frac{225}{484}$

Option 4: $\frac{7}{22}$

Question : If $\sec \theta=2 \frac{4}{23}$,find the value of $\tan^2 \theta$.

Option 1: $2 \frac{16}{529}$

Option 2: $1 \frac{200}{529}$

Option 3: $3 \frac{384}{529}$

Option 4: $3 \frac{177}{529}$

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 : If $\left(3 y+\frac{3}{y}\right)=8$, then find the value of $\left(y^2+\frac{1}{y^2}\right)$.

Option 1: $5\frac{1}{9}$

Option 2: $4\frac{5}{6}$

Option 3: $7\frac{1}{9}$

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