Assign $A, B, C, D$ from the given type of reaction.
$Mn(OH)_2 + H_2SO_4 \longrightarrow MnSO_4 + 2H_2O$

$A_2O_x$ is oxidized to $AO_3^-$ by $MnO_4^-$ in acidic medium. If $1.5 \times 10^{-3} \text{ mole}$ of $A_2O_x$ requires $40 \text{ mL}$ of $0.03 \text{ M } KMnO_4$ solution in acidic medium,which of the following statement$(s)$ is/are correct?

$PbO$ and $PbO_2$ react with $HCl$ according to the following chemical equations:
$(i)$ $2PbO + 4HCl \to 2PbCl_2 + 2H_2O$
$(ii)$ $PbO_2 + 4HCl \to PbCl_2 + Cl_2 + 2H_2O$
Why do these compounds differ in their reactivity?

$A$ sample $(5.6 \ g)$ containing iron is completely dissolved in cold dilute $HCl$ to prepare $250 \ mL$ of solution. Titration of $25.0 \ mL$ of this solution requires $12.5 \ mL$ of $0.03 \ M \ KMnO_4$ solution to reach the end point. The number of moles of $Fe^{2+}$ present in the $250 \ mL$ solution is $x \times 10^{-2}$ (consider complete dissolution of $FeCl_2$). The amount of iron present in the sample is $y \%$ by weight. (Assume: $KMnO_4$ reacts only with $Fe^{2+}$ in the solution. Use: Molar mass of iron as $56 \ g \ mol^{-1}$)
$(1)$ The value of $x$ is. . . . .
$(2)$ The value of $y$ is. . . . .

$x, y$ and $z$ are respectively:
$MnO_4^- + x e^- \xrightarrow{\text{Alkaline medium}} MnO_4^{2-}$
$MnO_4^- + y e^- \xrightarrow{\text{Acidic medium}} Mn^{2+}$
$MnO_4^- + z e^- \xrightarrow{\text{Neutral medium}} MnO_2$

What is a redox reaction? Explain its uses.