Step 1: Reaction with cold, dilute NaOH.
\[
\mathrm{Cl_2+2NaOH
\rightarrow
NaCl+NaOCl+H_2O}
\]
Here, chlorine changes from oxidation state \(0\) to \(-1\) and \(+1\).
Hence, disproportionation occurs.
Step 2: Reaction with hot, concentrated NaOH.
\[
3\mathrm{Cl_2}+6\mathrm{NaOH}
\rightarrow
5\mathrm{NaCl}+\mathrm{NaClO_3}+3\mathrm{H_2O}
\]
Chlorine changes from \(0\) to \(-1\) and \(+5\).
Hence, disproportionation also occurs.
Step 3: Reaction with \(\mathrm{H_2S}\).
\[
\mathrm{Cl_2+H_2S
\rightarrow
2HCl+S}
\]
Chlorine is only reduced from \(0\) to \(-1\), so no disproportionation occurs.
Step 4: Final conclusion.
Disproportionation occurs only in reactions I and II.
Hence, the correct option is
\[
\boxed{(A)}
\]