Assertion : The nature of the image formed by a concave mirror is real and inverted.
Reason: The image formed by a concave mirror depends on the position of the object at infinity.

Options

A. Both A and R are true R is the correct explanation of A.
B. Both A and R are true R is not the correct explanation of A.
C. A is true but R is false
D. A is false but R is true

Answer

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 "The nature of the image formed by a concave mirror is real and inverted."
- While it is true that a concave mirror can form real and inverted images, this is not the only type of image it can produce. A concave mirror can also produce virtual images depending on the position of the object. Therefore, the assertion is **false**.

2. **Understanding the Reason**:
- The reason states that "The image formed by a concave mirror depends on the position of the object at infinity."
- This statement is true because the nature of the image (real or virtual, inverted or upright) indeed depends on the position of the object relative to the mirror. For example:
- If the object is at infinity, the image is formed at the focus and is real and inverted.
- If the object is between the focus and the mirror, the image is virtual and upright.
- Thus, the reason is **true**.

3. **Conclusion**:
- Since the assertion is false and the reason is true, the overall statement is that the assertion does not support the reason. Therefore, the correct answer is that the assertion is false, and the reason is true.

### Final Answer:
- The assertion is **false** and the reason is **true**.