What is the volume (in litres) of oxygen at $STP$ required for complete combustion of $32 \ g$ of $CH_4$ ? (Molecular weight of $CH_4$ is $16$ )

If $u=f(r)$,where $r^2=x^2+y^2$,then $\left(\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}\right)$ is equal to

Which of the following exhibits moderate electrical conductivity?

If $f(x) = \sqrt{ax} + \frac{a^2}{\sqrt{ax}}$,then $f^{\prime}(a)$ is equal to

$A$ conducting rod of length $\ell$ is moving with velocity $v$ in a uniform magnetic field $B$ directed into the plane of the paper,as shown in the diagram. Which end of the rod is at a lower potential?

$\sim (p \vee q)$ is equal to