Alkaline oxidative fusion of MnO$_2$ gives 'X'. The products formed when 'X' undergoes disproportionation in acid medium are
I) KMnO$_4$
II) MnO$_2$
III) O$_2$
IV) H$_2$O
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In acid medium, disproportionation of manganate yields KMnO$_4$, MnO$_2$ and H$_2$O.
The fusion of MnO$_2$ with alkali produces manganate (MnO$_4^{2-}$), which disproportionates in acid to form permanganate (KMnO$_4$), MnO$_2$, and water (H$_2$O). O$_2$ is not a product.