1. Identify the reactions in a lead storage battery during charging

A lead storage battery is recharged by reversing the discharge reactions.

During discharge:

• Anode: Pb gets oxidized to $\text{PbSO}_4$
• Cathode: $\text{PbO}_2$ gets reduced to $\text{PbSO}_4$

So during charging, the reverse occurs:

• At anode (positive electrode during charging), $\text{PbSO}_4$ is oxidized to $\text{PbO}_2$
• At cathode (negative electrode during charging), $\text{PbSO}_4$ is reduced to Pb

2. Find oxidation state change at the anode

At the anode during charging: $\text{PbSO}_4 \rightarrow \text{PbO}_2$

• In $\text{PbSO}_4$, sulfate ion is $\text{SO}_4^{2-}$, so Pb must be $+2$
• In $\text{PbO}_2$, oxygen is $-2$ each, so Pb is $+4$

Thus at the anode, lead changes: $x_1 = +2, \quad y_1 = +4$

3. Find oxidation state change at the cathode

At the cathode during charging: $\text{PbSO}_4 \rightarrow \text{Pb}$

• In $\text{PbSO}_4$, Pb is $+2$
• In metallic Pb, oxidation state is $0$

Thus at the cathode, lead changes: $x_2 = +2, \quad y_2 = 0$

4. Compare with options

We obtained: $x_1, y_1, x_2, y_2 = +2, +4, +2, 0$

Now check the options:

• A: $0,+2,+4,+2$ ❌
• B: $+2,0,0,+4$ ❌
• C: $+4,+2,0,+2$ ❌
• D: $+2,0,+2,+4$ ❌

None of the given options matches the correct charging changes.

5. Why option D is incorrect

Option D says: $+2,0,+2,+4$

This would mean:

• anode: Pb goes from $+2$ to $0$
• cathode: Pb goes from $+2$ to $+4$

But during charging, oxidation occurs at the anode, so Pb should go from $+2$ to $+4$ there, not to $0$. Reduction occurs at the cathode, so Pb should go from $+2$ to $0$ there.

So the correct sequence should be: $+2,+4,+2,0$

which is not present among the listed options.