Question : If $\left(y^2+\frac{1}{y^2}\right)=167$ and $y>0$, find the value of $\left(y+\frac{1}{y}\right)$.

Option 1: 13

Option 2: $-\sqrt{165}$

Option 3: $\sqrt{165}$

Option 4: –13

Question : If $\cot A=\frac{5}{12}$, find the value of the following expression:
$\frac{5\left(1-\cos^2 A\right)}{6\left(1-\sin^2 A\right)}$

Option 1: $\frac{144}{5}$

Option 2: $\frac{24}{25}$

Option 3: $\frac{144}{25}$

Option 4: $\frac{24}{5}$

Question : If $\left(4y-\frac{4}{y}\right)=11$, find the value of $\left(y^2+\frac{1}{y^2}\right)$.

Option 1: $7 \frac{9}{16}$

Option 2: $5 \frac{9}{16}$

Option 3: $9 \frac{11}{16}$

Option 4: $9 \frac{9}{16}$

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