Preventing inclusion of air bubbles in a shrinkage dish is essential to obtain accurate test results. The correct way to prevent air bubbles is by mixing the soil with sufficient distilled water and making the soil pasty enough. This method ensures that the soil is properly compacted and eliminates the presence of air bubbles that can affect the test results.

Here is a detailed explanation of why option 'A' is the correct answer:

1. Importance of preventing air bubbles:
Air bubbles in the soil sample can significantly affect the shrinkage properties and test results. They can cause voids, uneven drying, and inaccurate measurements, leading to unreliable data. Therefore, it is crucial to prevent air bubbles during the preparation of the soil sample.

2. Mixing the soil with sufficient distilled water:
- Distilled water is used because it is free from impurities and contaminants that may affect the test results.
- Mixing the soil with water helps in achieving proper compaction and eliminating air voids. Water acts as a lubricant, allowing the soil particles to come closer and fill in the gaps.
- Sufficient water is added to ensure that the soil has the right moisture content for compaction. If the soil is too dry, it will be difficult to remove air bubbles, and if it is too wet, it may not provide accurate results.

3. Making the soil pasty enough:
- The soil should be mixed thoroughly with water until it reaches a pasty consistency. This means that the soil should be wet enough to hold its shape but not excessively saturated.
- A pasty soil consistency helps in achieving proper compaction and minimizing the formation of air voids.
- It is important to note that the soil should not be too liquid or too dry, as both conditions can lead to the inclusion of air bubbles.

4. Alternatives:
- Option 'B' suggests coating the surface with a thin layer of oil. While this technique can help in reducing water evaporation during the test, it does not directly address the prevention of air bubbles. Oil may not effectively displace air bubbles, and it may introduce other contaminants that can affect the test results.
- Option 'C' states that all of the mentioned methods are correct, but this is not accurate. Only option 'A' provides the appropriate method for preventing air bubbles in a shrinkage dish.
- Option 'D' suggests that none of the mentioned methods are correct, which is incorrect as option 'A' is the correct method.

In conclusion, the correct method for preventing the inclusion of air bubbles in a shrinkage dish is by mixing the soil with sufficient distilled water and making the soil pasty enough. This ensures proper compaction, eliminates air voids, and provides accurate test results.