The method of zone refining of metals is based on the principle of

Which of the following isomerism is not possible for complexes having molecular formulae?
$(I) Pt(SCN)_2 \cdot 3PEt_3$,$(II) CoBr \cdot SO_4 \cdot 5NH_3$,$(III) FeCl_2 \cdot 6H_2O$

Two identical condensers $M$ and $N$ are connected in series with a battery. The space between the plates of $M$ is completely filled with a dielectric medium of dielectric constant $8$,and a copper plate of thickness $d/2$ is introduced between the plates of $N$ ($d$ is the distance between the plates). Then the potential differences across $M$ and $N$ are,respectively,in the ratio:

Two nuclei have their mass numbers in the ratio of $1:3$. The ratio of their densities would be

Oxidation number of $P$ in $Mg_2P_2O_7$ is

If $x^y=y^x$, then $x(x-y \log x) \frac{d y}{d x}$ is equal to :