If $\sin ^{-1}\left(\frac{x}{13}\right)+\operatorname{cosec}^{-1}\left(\frac{13}{12}\right)=\frac{\pi}{2}$, then the value of

The graphical solution set of the system of inequations $2 x+3 y \leq 6, x+4 y \geq 4, x \geq 0, y \geq 0$ is given by

The derivative of $\sin ^{-1}\left(2 x \sqrt{1-x^2}\right)$ w.r.t. $\sin ^{-1}\left(3 x-4 x^3\right)$ is

If $A=\left[\begin{array}{cc}5 a & -b \\ 3 & 2\end{array}\right]$ and $A \cdot \operatorname{adj} A=A A^T$, then $5 a+b$ is equal to