Step 1: Grasping the carbylamine reaction.
The carbylamine test serves to detect primary amines by reacting them with chloroform and alcoholic KOH to generate foul-smelling isocyanides: RNH₂ + CHCl₃ + 3KOH → RNC + 3KCl + 3H₂O.
Step 2: Evaluating the choices.
R₂NH is a secondary amine and does not respond to this test. RNH₂ is a primary amine and gives a positive result. RNC is the product formed, not the reacting amine. RCN is a nitrile and fails the test.
Step 3: Final verdict.
Only primary amines yield a positive carbylamine test, so the answer is RNH₂.