Step 1: Recall substituent effects.
- Electron-donating groups (EDG) decrease the C=O stretching frequency by stabilizing the carbonyl resonance.
- Electron-withdrawing groups (EWG) increase the C=O stretching frequency by reducing resonance stabilization, making the bond stronger.
Step 2: Apply to given groups.
- p-amino (EDG): Strongly donates electrons → lowers frequency → 1677 cm\(^{-1}\).
- p-nitro (EWG): Strongly withdraws electrons → raises frequency → 1700 cm\(^{-1}\).
- p-methoxy (EDG but weaker than amino): Slight lowering effect → 1684 cm\(^{-1}\).
Step 3: Match.
P-1, Q-2, R-3.
Final Answer:
\[
\boxed{P-1,\; Q-2,\; R-3}
\]