`{:(,"List-I",,"List-II"),(P,"Source and listener are moving in same",1.,"Longitudinal waves"),(,"direction with same velocity.",,),(Q,"Source and listener are moving away from",2.,"Apparent frequency increases"),(,"each other.",,),(R,"Source is moving towards the listener at rest",3.,"No change in frequency"),(S,"Sound waves in air",4.,"Apparent frequency decreases"):}`

Options

A. `{:(P,Q,R,S),(1,2,3,4):}`
B. `{:(P,Q,R,S),(2,3,1,4):}`
C. `{:(P,Q,R,S),(2,3,4,1):}`
D. `{:(P,Q,R,S),(3,4,2,1):}`

Answer

To solve the problem of matching the elements of List-I with List-II, we need to analyze each statement in List-I and determine the corresponding statement in List-II based on the principles of wave motion and the Doppler effect.

### Step-by-Step Solution:

1. **Analyzing Statement P**:
- **Statement**: "Source and listener are moving in the same direction with the same velocity."
- **Analysis**: When both the source and listener move at the same velocity in the same direction, there is no relative motion between them. Thus, the apparent frequency remains unchanged.
- **Conclusion**: The answer for P is **3 (No change in frequency)**.

2. **Analyzing Statement Q**:
- **Statement**: "Source and listener are moving away from each other."
- **Analysis**: When the source and listener are moving away from each other, the apparent frequency decreases. The formula for apparent frequency shows that as the distance increases, the frequency observed is less than the original frequency.
- **Conclusion**: The answer for Q is **4 (Apparent frequency decreases)**.

3. **Analyzing Statement R**:
- **Statement**: "Source is moving towards the listener at rest."
- **Analysis**: When the source approaches a stationary listener, the apparent frequency increases. The formula indicates that the frequency observed will be greater than the original frequency due to the source moving closer.
- **Conclusion**: The answer for R is **2 (Apparent frequency increases)**.

4. **Analyzing Statement S**:
- **Statement**: "Sound waves in air."
- **Analysis**: Sound waves are classified as longitudinal waves because the particles of the medium (air) vibrate in the same direction as the wave travels, creating compressions and rarefactions.
- **Conclusion**: The answer for S is **1 (Longitudinal waves)**.

### Final Matching:
- P → 3 (No change in frequency)
- Q → 4 (Apparent frequency decreases)
- R → 2 (Apparent frequency increases)
- S → 1 (Longitudinal waves)

Thus, the correct matches are:
- P - 3
- Q - 4
- R - 2
- S - 1

### Final Answer:
The correct option is **4** (P-3, Q-4, R-2, S-1).