Step 1: Understanding the Concept:
Primary, secondary and tertiary amines differ in how many hydrogens sit on nitrogen. A reaction needing two N-H hydrogens can be given only by a primary amine.
Step 2: Check option (A).
Acetylation replaces an N-H hydrogen with an acetyl group. Primary and secondary amines both do this. Not unique.
Step 3: Check option (B).
Alkylation of the nitrogen works with primary, secondary and even tertiary amines (to give quaternary salts). Not unique.
Step 4: Check option (C).
Nitrous acid reacts with all three classes, although the products differ. Not unique.
Step 5: Check option (D).
In the carbylamine test, a primary amine is heated with chloroform and alcoholic KOH to give a foul smelling isocyanide.
\[ \text{RNH}_2 + \text{CHCl}_3 + 3\text{KOH} \to \text{RNC} + 3\text{KCl} + 3\text{H}_2\text{O} \]
Secondary and tertiary amines do not give it. So (D) is the answer.
Final Answer:
Only primary amines give the carbylamine test, option (D).
\[ \boxed{\text{Carbylamine test}} \]