$H_2O_2$ with $KMnO_4$ in acidic medium gives a manganese compound 'X' and in basic medium gives another manganese compound 'Y'. The oxidation states of manganese in X and Y respectively are:
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Remember: In acidic medium, $KMnO_4$ gives Mn$^{2+}$; in basic or neutral medium, it gives MnO$_2$.
In acidic medium, $KMnO_4$ (Mn in +7 oxidation state) is reduced to Mn$^{2+}$ (oxidation state = +2).
In basic medium, $KMnO_4$ is reduced to MnO$_2$ where Mn has oxidation state +4.