Step 1: Analyze Option (A) - Iodoform Test:
Reagent: \( \text{I}_2 + \text{NaOH} \).
This test detects the presence of \( \text{CH}_3\text{-CH(OH)-} \) group or \( \text{CH}_3\text{-CO-} \) group.
- Ethanol (\( \text{CH}_3\text{CH}_2\text{OH} \)) has the \( \text{CH}_3\text{-CH(OH)-} \) group. It gives a positive Iodoform test (yellow ppt).
- Methanol (\( \text{CH}_3\text{OH} \)) does not.
Thus, they can be distinguished. Match is correct.
Step 2: Analyze Option (B) - Lucas Test:
Reagent: Lucas Reagent (ZnCl$_2$ + HCl).
Distinguishes primary, secondary, and tertiary alcohols based on turbidity time.
- Ethanol is a $1^\circ$ alcohol (No turbidity at room temp).
- tert-Butyl alcohol is a $3^\circ$ alcohol (Immediate turbidity).
Thus, they can be distinguished. Match is correct.
Step 3: Analyze Option (C) - Reaction with Sodium:
Reagent: Sodium metal (Na).
Reacts with acidic hydrogen (terminal alkynes).
- Propyne (\( \text{CH}_3-\text{C}\equiv\text{CH} \)) has an acidic terminal hydrogen. Reacts with Na to release \( \text{H}_2 \) gas.
- But-2-yne (\( \text{CH}_3-\text{C}\equiv\text{C}-\text{CH}_3 \)) has no acidic hydrogen. No reaction.
Thus, they can be distinguished. Match is correct.
Step 4: Analyze Option (D) - 2,4-DNP Test:
Reagent: 2,4-Dinitrophenylhydrazine.
This is a general test for the Carbonyl group (Aldehydes and Ketones).
- Acetaldehyde (\( \text{CH}_3\text{CHO} \)) is an aldehyde. It gives an orange-red ppt.
- Acetone (\( (\text{CH}_3)_2\text{CO} \)) is a ketone. It also gives an orange-red ppt.
Since both give a positive test, 2,4-DNP cannot distinguish between them. (Tollens' or Fehling's reagent would be needed).
Thus, the match is incorrect.