Question : What is the expansion of $(2+\frac{1}{p})^2$?

Option 1: $4+\frac{4}{p}+\frac{1}{p^2}$

Option 2: $2+\frac{2}{p}+\frac{1}{p^2}$

Option 3: $2+\frac{4}{p}+\frac{1}{p^2}$

Option 4: $4+\frac{2}{p}+\frac{1}{p^2}$

Question : What is the expansion of $\left(1-\frac{1}{p}\right)^2$?

Option 1: $1+\frac{2}{p}-\frac{1}{p^2}$

Option 2: $1-\frac{2}{p}+\frac{1}{p^2}$

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

Option 4: $1+\frac{2}{p}+\frac{1}{p^2}$

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 $\frac{4}{3}\left(\sin ^2 35^{\circ}+\sin ^2 55^{\circ}\right) ?$

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

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

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

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

Question : 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 : Simplify: $\sqrt{\frac{4\frac{1}{7}-2\frac{1}{4}}{3\frac{1}{2}+1\frac{1}{7}}+\frac{2}{2+\frac{1}{2+\frac{1}{5-\frac{1}{5}}}}}$

Option 1: $1$

Option 2: $4$

Option 3: $\sqrt{\frac{159}{130}}$

Option 4: $2$