Step 1: Think of what is needed.
The carbylamine reaction needs the group $\text{-NH}_2$, because both hydrogens are removed to form the isocyanide.
Step 2: Test each reaction.
Acetylation, alkylation and reaction with nitrous acid occur for more than one class of amine.
Step 3: Conclude.
Only the carbylamine test is exclusive to primary amines, so option (D).
Final Answer:
Option (D).
\[ \boxed{\text{Carbylamine test}} \]