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 $2 \frac{3}{5} \div\left[2 \frac{1}{3} \div\left\{4 \frac{1}{3}-\left(2 \frac{1}{2}+\frac{2}{3}\right)\right\}\right]$ is equal to:

Option 1: $1 \frac{3}{10}$

Option 2: $2 \frac{7}{10}$

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

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

Question : If $\left(a+\frac{1}{a}\right)=6$, then what is the value of $\frac{3}{4}\left(a^2+\frac{1}{a^2}\right)$?

Option 1: 22.5

Option 2: 34

Option 3: 25.5

Option 4: 36

Question : If $3a^{2}= b^{2}\neq0$, then the value of $\frac{\left (a+b \right)^{3}-\left (a-b \right)^{3}}{\left (a+b \right)^{2}+\left (a-b \right)^{2}}$ is:

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

Option 2: $b$

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

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

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

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: $\frac{3}{4}$