The pair of compounds,which cannot exist together in a solution is

In which interval is the function $f(x) = 2x^2 - \ln |x|, (x \neq 0)$ monotonically decreasing?

The electric potential $V$ at any point $(x, y, z)$ (all in $m$) in space is given by $V = 4x^2 \, V$. The electric field at the point $(1 \, m, 0, 2 \, m)$ in $V/m$ is:

Let $P = \{\theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta\}$ and $Q = \{\theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta\}$ be two sets,then:

The value of $\cos ^{-1} \left[ \cot \left\{ \sin ^{-1} \sqrt{\frac{2 - \sqrt{3}}{4}} + \cos ^{-1} \frac{\sqrt{12}}{4} + \sec ^{-1} \sqrt{2} \right\} \right]$ is

Two closed organ pipes of length $100\,cm$ and $101\,cm$ long give $16$ beats in $20\,sec$ when each pipe is sounded in fundamental mode. Calculate the velocity of sound in $m/s$.