One of the products formed due to the reaction between $KMnO_4$ and $HCl$ is

Balance the following redox reactions by the ion-electron method:
$(a)$ $MnO_{4(aq)}^- + I_{(aq)}^- \to MnO_{2(s)} + I_{2(s)}$ (in basic solution)
$(b)$ $MnO_{4(aq)}^- + SO_{2(g)} \to Mn_{(aq)}^{2+} + HSO_{4(aq)}^-$ (in acidic solution)
$(c)$ $H_2O_{2(aq)} + Fe_{(aq)}^{2+} \to Fe_{(aq)}^{3+} + H_2O_{(l)}$ (in acidic solution)
$(d)$ $Cr_2O_7^{2-} + SO_{2(g)} \to Cr_{(aq)}^{3+} + SO_{4(aq)}^{2-}$ (in acidic solution)

$Na_2S_2O_3$ reacts with moist $Cl_2$ to form $Na_2SO_4$, $HCl$, and $X$. Which one of the following is $X$?

Treatment of alkaline $KMnO_{4}$ solution with $KI$ solution oxidises iodide to:

Write the balanced chemical equations for the following reactions:
$(1)$ Reaction between $MnO_4^-$ and $I^-$ in neutral or faintly alkaline solution.
$(2)$ Reaction between $MnO_4^-$ and $C_2O_4^{2-}$ in acidic medium $(H^+)$.

Observe the following reaction:
$xS_{8\text{(s)}} + yOH^{-}{_{\text{(aq)}}} \rightarrow zS^{2-}{_{\text{(aq)}}} + 2S_2O_3^{2-}{_{\text{(aq)}}} + 6H_2O_{\text{(l)}}$
Find the values of $x, y$ and $z$ respectively.