Step 1: Understanding Electrophilic Substitution.
In electrophilic aromatic substitution reactions, electron-donating groups increase the reactivity of the aromatic ring, while electron-withdrawing groups decrease it. The amino group \( NH_2 \) is an electron-donating group, the nitro group \( NO_2 \) is electron-withdrawing, and the carboxyl group \( COOH \) is also electron-withdrawing. Therefore, the order of reactivity is \( B>A>C \).
Step 2: Conclusion.
The correct answer is (C), \( B>A>C \).