A solution containing $1{\mathrm{molL}}^{-1}$ of each of $\mathrm{Cu}{\left({\mathrm{NO}}_3\right)}_2,{\mathrm{AgNO}}_3$ and $\mathrm{Mg}{\left({\mathrm{NO}}_3\right)}_2$ is being electrolysed by using inert electrodes. If $E^{\circ }\left({\mathrm{Ag}}^{+}\mid \mathrm{Ag}\right)=0.80\mathrm{V},E^{\circ }\left({\mathrm{Cu}}^{2+}\mid \mathrm{Cu}\right)=0.34\mathrm{V}$and $E^{\circ }\left({\mathrm{Mg}}^{2+}\mid \mathrm{Mg}\right)=-2.37\mathrm{V}$, the sequence of deposition of metals on the cathode with increasing voltage would be

The propensity for deposition increases with decrease voltage.

Mg has a negative reduction potential, therefore it has no inclination to deposit and cannot be produced by electrolyzing aqueous salt solutions. Reduction potential order is Mg> Cu> Ag, so they decompose in that order.

Hence option B is correct