Question : If $A+\frac{1}{1+\frac{1}{2+\frac{1}{3}}}=\frac{9}{10}$, then the value of A is:

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

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

Option 3: $\frac{2}{5}$

Option 4: $\frac{1}{10}$

Question : If $2A=3B$, then what is the value of $\frac{A+B}{A}$?

Option 1: $\frac{5}{4}$

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

Option 3: $\frac{5}{2}$

Option 4: $\frac{5}{3}$

Question : If $a-\frac{1}{a}=4$, then the value of $a+\frac{1}{a}$ is:

Option 1: $5 \sqrt{5}$

Option 2: $4 \sqrt{5}$

Option 3: $2 \sqrt{5}$

Option 4: $3 \sqrt{5}$

Question : If $\tan A=\frac{4}{3}, 0 \leq A \leq 90^{\circ}$, then find the value of $\sin A$.

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

Option 2: $1$

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

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

Question : If $\tan A=\frac{2}{5}$, then find the value of $\frac{\sec ^2 A}{\operatorname{cosec}^2 A}$.

Option 1: $\frac{2}{5}$

Option 2: $\frac{4}{25}$

Option 3: $\frac{9}{25}$

Option 4: $\frac{3}{5}$