Step 1: Concept
Acidity of substituted benzoic acids is increased by Electron Withdrawing Groups (EWG) and decreased by Electron Donating Groups (EDG).
Step 2: Meaning
Nitro ($-NO_2$) is a strong EWG ($-I$ and $-M$ effects). Methoxy ($-OCH_3$) is an EDG due to the $+M$ effect.
Step 3: Analysis
4-Nitrobenzoic acid (C) is the most acidic due to the stable carboxylate ion formed by the EWG. 4-Methoxybenzoic acid (B) is the least acidic because the EDG destabilizes the carboxylate ion. Benzoic acid (A) is the reference point.
Step 4: Conclusion
The correct increasing order of acidity is: 4-Methoxybenzoic acid < Benzoic acid < 4-Nitrobenzoic acid (B < A < C).
{red}{Final Answer: (A)