Step 1: Match dil KMnO$_4$ \text{with List-II.}
Dilute potassium permanganate (KMnO\(_4\)) is commonly used to test for unsaturation (double bonds) in compounds.
It is a strong oxidizing agent that decolorizes when it reacts with unsaturated compounds.
Thus, A-I is correct (Unsaturation test).
Step 2: Match FeCl$_3$ \text{with List-II.}
Ferric chloride (FeCl\(_3\)) reacts with phenolic compounds to form a colored complex.
This test is used to identify the presence of the phenolic -OH group.
Thus, B-III is correct (Phenolic -OH).
Step 3: Match Liberate CO$_2$ \text{with NaHCO$_3$} \text{with List-II.}
The liberation of CO\(_2\) with NaHCO\(_3\) (sodium bicarbonate) is a characteristic test for carboxylic acids, as carboxylic acids react with bicarbonates to release CO\(_2\).
Thus, C-IV is correct (Carboxylic acid).
Step 4: Match Ceric Ammonium Nitrate Test.
The Ceric Ammonium Nitrate test is used to detect alcohols, specifically alcoholic -OH groups, as it forms a red complex with alcohols.
Thus, D-II is correct (Alcoholic -OH).