Assertion. Different gases at the same conditions of temperature and pressure have same root mean velocity.
Reason. Root mean square velocity lies between average velocity and most probable velocity.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that different gases at the same conditions of temperature and pressure have the same root mean square (RMS) velocity.

- The formula for root mean square velocity (VRMS) is given by:
\[ V_{RMS} = \sqrt{\frac{3RT}{M}} \]
where \( R \) is the gas constant, \( T \) is the temperature in Kelvin, and \( M \) is the molar mass of the gas.

2. **Analyzing the Assertion**:
- At the same temperature (T) and pressure (P), the value of \( R \) is constant, but the molar mass \( M \) varies for different gases.
- Therefore, since \( M \) is different for different gases, the root mean square velocity \( V_{RMS} \) will also be different for different gases.
- Thus, the assertion is **false**.

3. **Understanding the Reason**:
The reason states that the root mean square velocity lies between the average velocity and the most probable velocity.

- The formulas for average velocity (V_avg) and most probable velocity (V_mp) are:
\[ V_{avg} = \sqrt{\frac{8RT}{\pi M}} \]
\[ V_{mp} = \sqrt{\frac{2RT}{M}} \]
- To compare these velocities, we can derive their ratios:
\[ V_{mp} : V_{avg} : V_{RMS} = 1 : 1.128 : 1.224 \]
- This indicates that \( V_{RMS} \) is indeed the highest, while \( V_{mp} \) is the lowest.

4. **Analyzing the Reason**:
- Since \( V_{RMS} \) is not between \( V_{avg} \) and \( V_{mp} \) but is actually the highest, the reason is also **false**.

5. **Conclusion**:
- Both the assertion and the reason are false. Therefore, the correct option is that both statements are incorrect.

### Final Answer:
Both the assertion and the reason are false.

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