How many electrons $(e^-)$ are gained by the oxidizing agent $KMnO_4$ to convert into $MnO_4^{2-}$,$MnO_2$,$Mn_2O_3$,and $Mn^{2+}$ respectively?

Aqueous sulphite reacts with dilute sulphuric acid to form $X_{(g)}$. The liberated $X_{(g)}$ is passed into acidified $KMnO_4$ solution. What is the oxidation state of $Mn$ in the product formed?

$AgCl$ on fusion with $Na_2CO_3$ forms

The unbalanced chemical reactions given in List-$I$ show missing reagent or condition $(?)$ which are provided in List-$II$. Match List-$I$ with List-$II$ and select the correct answer using the code given below the lists:

List-$I$	List-$II$
$P. \ PbO_2 + H_2SO_4 \xrightarrow{?} PbSO_4 + O_2 + \text{other product}$	$1. \ NO$
$Q. \ Na_2S_2O_3 + H_2O \xrightarrow{?} NaHSO_4 + \text{other product}$	$2. \ I_2$
$R. \ N_2H_4 \xrightarrow{?} N_2 + \text{other product}$	$3. \ \text{Warm}$
$S. \ XeF_2 \xrightarrow{?} Xe + \text{other product}$	$4. \ Cl_2$

Codes: $P \quad Q \quad R \quad S$

Which one of the following reactions is not possible?

$A$ 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. . . . .