If $$\log _2 x+\log _4 x+\log _8 x+\log _{16} x=\frac{25}{36}$$ and $$x=2^{\mathrm{k}}$$ then $$\mathrm{k}$$ is

If $$\left|\begin{array}{ccc}\cos (A+B) & -\sin (A+B) & \cos (2 B) \\ \sin A & \cos A & \sin B \\ -\cos A & \sin A & \cos B\end{array}\right|=0$$, then the value of $$B$$ is

General solution of the differential equation $$\log \left(\frac{d y}{d x}\right)=a x+b y$$ is

$$\int(\sqrt{\tan x}+\sqrt{\cot x}) d x=$$