Concept:
In aqueous medium, the basic strength of aliphatic amines depends on:
• electron releasing effect of alkyl groups
• solvation of the protonated amine
Because of the balance between these two effects, the order in aqueous medium is commonly:
\[
2^\circ > 1^\circ > 3^\circ > \text{NH}_3
\]
Step 1: Compare the given bases.
• \(\text{NH}_3\) has no alkyl group.
• \(\text{CH}_3\text{NH}_2\) is primary amine.
• \((\text{CH}_3)_2\text{NH}\) is secondary amine.
• \((\text{CH}_3)_3\text{N}\) is tertiary amine.
Step 2: Use the order in aqueous medium.
In water, secondary amine is strongest because it gets good +I effect and still gets sufficient solvation.
So the strongest base is:
\[
(\text{CH}_3)_2\text{NH}
\]
Hence, the correct answer is:
\[
\boxed{(C)\ (\text{CH}_3)_2\text{NH}}
\]