Step 1: Understanding basicity of amines.
The basicity of amines depends on the electron-donating effect of the alkyl group attached to the nitrogen. Alkyl groups increase the electron density on nitrogen, making the amine more basic.
Step 2: Analysis of options.
(A) \( \text{C}_6\text{H}_5\text{NH}_2 \): Aniline (C₆H₅NH₂) has a phenyl group, which is electron-withdrawing, thus making it less basic than alkyl amines.
(B) Another form of \( \text{C}_6\text{H}_5\text{NH}_2 \): Same reasoning as (A), still less basic.
(C) \( \text{C}_2\text{H}_5\text{NH}_2 \): Ethylamine (C₂H₅NH₂) is more basic because the ethyl group is electron-donating.
(D) Another form of \( \text{C}_2\text{H}_5\text{NH}_2 \): Same reasoning as (C), still more basic.
Step 3: Conclusion.
The correct answer is (C) because \( \text{C}_2\text{H}_5\text{NH}_2 \) (ethylamine) is the most basic due to the electron-donating effect of the ethyl group.