$2 \text{ mol}$ of $FeSO_4$ are oxidized by $X \text{ mol}$ of $KMnO_4$ whereas $2 \text{ mol}$ of $FeC_2O_4$ are oxidized by $Y \text{ mol}$ of $KMnO_4$. The ratio of $X$ and $Y$ is:

Balance the following equations by the oxidation number method:
$(a) Fe^{+2} + H^{+} + Cr_2O_7^{-2} \to Cr^{+3} + Fe^{+3} + H_2O$
$(b) I_2 + NO_3^- \to NO_2 + IO_3^-$
$(c) I_2 + S_2O_3^{-2} \to I^{-} + S_4O_6^{-2}$
$(d) MnO_4^- + C_2O_4^{-2} \to Mn^{+2} + CO_2$

How do you account for the following observations?
$(a)$ Though alkaline potassium permanganate and acidic potassium permanganate both are used as oxidants,yet in the manufacture of benzoic acid from toluene,we use alcoholic potassium permanganate as an oxidant. Why? Write a balanced redox equation for the reaction.
$(b)$ When concentrated sulphuric acid is added to an inorganic mixture containing chloride,we get a colourless pungent-smelling gas $HCl$,but if the mixture contains bromide,then we get red vapour of bromine. Why?

Match the following columns:-

Column-$I$ [Type of reaction]	Column-$II$ [Example]
$I$. Intermolecular redox reaction	$A$. $CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O$
$II$. Intramolecular redox reaction	$B$. $NH_4NO_2 \rightarrow N_2 + 2H_2O$
$III$. Disproportionation reaction	$C$. $2H_2O_2 \rightarrow 2H_2O + O_2$
$IV$. Comproportionation reaction	$D$. $KClO_3 \rightarrow KCl + \frac{3}{2}O_2$

Assign $A, B, C, D$ from the given type of reaction.
$2KI + HgI_2 \downarrow \longrightarrow K_2[HgI_4]$

Potassium permanganate works as an oxidising agent both in acidic and basic medium. In both states,the products obtained by $KMnO_4$ are respectively: