- For \( A \), the reaction \( \text{H}_2\text{C} = \text{CH}_2 \) with \( \text{Hg}_2^{2+}, H_2O \) forms a carboxylic acid, which corresponds to option III, \( \text{HCOOH} \).
- For \( B \), \( \text{CH}_3\text{Cl} \) reacts with \( \text{O}_2 \) in the presence of \( \text{MnO}_2 \), yielding \( \text{CH}_3\text{COOH} \), which corresponds to option IV.
- For \( C \), \( \text{H}_2\text{C} = \text{CH}_2 \) reacts with \( \text{O}_3 \) in the presence of \( \text{Zn} \), and water, forming formic acid \( \text{HCOOH} \), matching with option II.
- For \( D \), \( \text{CH}_3\text{Cl} \) in the presence of \( \text{KMnO}_4 \) and \( H^+ \) forms acetic acid, matching with option I.
Thus, the correct match is option 2.