Alkaline oxidative fusion of MnO _ 2 gives " A " which on...

The alkaline oxidative fusion is a redox reaction (undergoes both oxidation and reduction simultaneously) in which a compound undergoes fusion with itself only, in the presence of a base or an alkaline solution. 

Electrolysis is a chemical process where an electric current is passed through an electrolyte, causing a non-spontaneous chemical reaction to occur, typically resulting in the decomposition of the electrolyte into its constituent elements or ions.

Alkaline oxidative fusion of ${MnO}_{2}$ :
$2{MnO}_{2} + 4{OH}^{-} + {O}_{2} \to 2{MnO}_{4}^{2 -} + 2{H}_{2}O$

Electrolytic oxidation of ${MnO}_{4}^{2 -}$ in alkaline medium.
${MnO}_{4}^{2 -} \to {MnO}_{4}^{-} + {e}^{-}$

Hence, the answer is option B.