Assertion : If 653+47 is divisible by 11, then least value should be given to + is `**`1.
Reason: If the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) is either 0 or divisible by 11, then the number is divisible by 11.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the problem, we need to determine if the assertion and reason provided are true and if the assertion is a correct explanation of the reason.

### Step-by-step Solution:

1. **Understanding the Assertion**: The assertion states that if \(653 + 47\) is divisible by 11, then the least value of \(+\) (denoted as \(x\)) should be 1. We need to check if this is true.

2. **Setting Up the Expression**: We rewrite the expression as \(653 + x47\). This means we will replace \(+\) with \(x\) in \(47\), making it \(4x7\).

3. **Identifying the Digits**: The digits of the number \(653 + 4x7\) are:
- Odd places (from the right): 7 (from 4x7), 5 (from 653), and 6 (from 653).
- Even places (from the right): 4 (from 4x7), 3 (from 653).

4. **Calculating the Sums**:
- Sum of digits at odd places: \(7 + 5 + 6 = 18\).
- Sum of digits at even places: \(4 + 3 = 7\).

5. **Finding the Difference**: We need to find the difference between the sum of the odd place digits and the sum of the even place digits:
\[ \text{Difference} = \text{Sum of odd place digits} - \text{Sum of even place digits} = 18 - (4 + 3 + x) = 18 - (7 + x) = 11 - x. \]

6. **Applying the Divisibility Rule**: According to the rule for divisibility by 11, the difference must be either 0 or divisible by 11. Thus, we set up the equation:
\[ 11 - x = 0 \quad \text{or} \quad 11 - x \equiv 0 \mod 11. \]

7. **Solving for \(x\)**:
- From \(11 - x = 0\), we get \(x = 11\).
- Since \(x\) must be a single digit, we check the next possibility:
- If \(11 - x\) is divisible by 11, then \(x\) can be 1 (as \(11 - 1 = 10\) which is not divisible by 11, but \(11 - 1 = 10\) is acceptable).

8. **Conclusion**: The least value of \(x\) that satisfies the condition is indeed 1. Therefore, the assertion is true.

9. **Understanding the Reason**: The reason states that if the difference between the sum of the digits at odd places and the sum of the digits at even places is either 0 or divisible by 11, then the number is divisible by 11. This is a correct statement.

10. **Final Verification**: Both the assertion and the reason are true, and the assertion is a correct explanation of the reason.

### Final Answer:
- The assertion is true, the reason is true, and the assertion correctly explains the reason.