Analyze Statement I

We compare two permanganate titrations in acidic medium:

• Oxalic acid vs. $\mathrm{KMnO_4}$ in dilute $\mathrm{H_2SO_4}$
• FAS ($\mathrm{Fe^{2+}}$) vs. $\mathrm{KMnO_4}$ in dilute $\mathrm{H_2SO_4}$

The relevant reactions are:

$2\mathrm{MnO_4^-} + 5\mathrm{C_2O_4^{2-}} + 16\mathrm{H^+} \rightarrow 2\mathrm{Mn^{2+}} + 10\mathrm{CO_2} + 8\mathrm{H_2O}$

and

$\mathrm{MnO_4^-} + 5\mathrm{Fe^{2+}} + 8\mathrm{H^+} \rightarrow \mathrm{Mn^{2+}} + 5\mathrm{Fe^{3+}} + 4\mathrm{H_2O}$

• The oxidation of oxalic acid/oxalate by permanganate is slow at room temperature.
• Hence, the oxalic acid titration is started warm, around $60^\circ\mathrm{C}$.
• In contrast, oxidation of $\mathrm{Fe^{2+}}$ by permanganate is sufficiently fast at room temperature, so no initial heating is required.

Therefore, Statement I is true.

Analyze Statement II

• In oxalic acid vs. $\mathrm{KMnO_4}$ titration, the reaction is initially slow.
• As the reaction begins, $\mathrm{Mn^{2+}}$ is produced (present as $\mathrm{MnSO_4}$ in sulfuric acid medium).
• This $\mathrm{Mn^{2+}}$ acts as an autocatalyst, accelerating the reaction.
• Initial warming helps generate enough $\mathrm{Mn^{2+}}$ to start this catalytic cycle.

So the first part of Statement II is correct.

Now for FAS:

• On heating, $\mathrm{Fe^{2+}}$ can get oxidized by atmospheric oxygen to $\mathrm{Fe^{3+}}$.
• This changes the amount of reductant actually available for titration and introduces error.
• Therefore FAS titration is not heated.

Hence, Statement II is also true.

Choose the correct option

Since both statements are true:

$\boxed{\text{Option C}}$

Compare with stored correct answer

• Derived answer: C
• Stored correct answer: C

They match.