How many moles of $H_2O_2$ are required to decolorize $1 \ mol$ of $KMnO_4$ in an acidic medium (in $.5$)?

Which of the following reagents causes the aqueous colored solution of acidic $KMnO_4$ to become colorless?

The number of moles of acidified $KMnO_4$ required to convert one mole of sulphite ion into sulphate ion is

$KMnO_4$ acts as an oxidising agent in acidic medium. The number of moles of $KMnO_4$ that will be needed to react with one mole of sulphide ion $(S^{2-})$ in acidic solution is . . . . . . (in $/5$)?

The reaction of sulphur in alkaline medium is given below:
$S_{8(s)} + a OH^{-}_{(aq)} \rightarrow b S^{2-}_{(aq)} + c S_{2}{O_{3}}^{2-}_{(aq)} + d H_{2}O_{(\ell)}$
The value of '$a$' is ............ (Integer answer)

Assign $A$,$B$,$C$,$D$ from the given type of reaction.
$(NH_4)_2Cr_2O_7 \xrightarrow{\Delta} N_2 \uparrow + Cr_2O_3 \downarrow + 4H_2O \uparrow$