Question : If $a+\frac{1}{a}=P^2$, then find $a^2+\frac{1}{a^2}$.

Option 1: $p^2 - 2$

Option 2: $p^2 + 2$

Option 3: $p^4 - 2$

Option 4: $p^4 + 2$

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 $\frac{2 \sin A-\cos A}{\sin A+\cos A}=1$, then find the value of $\cot A$.

Option 1: $1$

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

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

Option 4: $2$

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: $\frac{3}{5}$

Question : If $a, b, c$ are all non-zero and $a+b+c=0$, then find the value of $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{ab}$.

Option 1: $3$

Option 2: $4$

Option 3: $1$

Option 4: $\frac{1}{2}$

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: $\frac{1}{10}$