At high temperature , boron burns in air to give a mixture of `B_2 O_3` and BN.

Answer

To determine whether the statement "At high temperature, boron burns in air to give a mixture of B₂O₃ and BN" is true or false, we can analyze the reactions that occur when boron is burned in air.

### Step-by-Step Solution:

1. **Understanding the Components of Air**:
- Air is primarily composed of nitrogen (N₂) and oxygen (O₂), along with trace amounts of other gases.

2. **Reactions of Boron with Oxygen**:
- When boron (B) is heated in the presence of oxygen, it reacts to form boron trioxide (B₂O₃).
- The balanced chemical reaction for this process is:
\[ 4B + 3O₂ \rightarrow 2B₂O₃ \]

3. **Reactions of Boron with Nitrogen**:
- Boron can also react with nitrogen in the air to form boron nitride (BN).
- The balanced chemical reaction for this process is:
\[ 2B + N₂ \rightarrow 2BN \]

4. **Combining the Reactions**:
- Since air contains both nitrogen and oxygen, when boron burns in air at high temperatures, it can react with both gases simultaneously.
- This results in the formation of a mixture of boron trioxide (B₂O₃) and boron nitride (BN).

5. **Conclusion**:
- Therefore, the statement that "At high temperature, boron burns in air to give a mixture of B₂O₃ and BN" is true.

### Final Answer:
The statement is **True**.