In each of the following numbers. Replace `**` by the smallest number to make it divisible by 9 :
(i) ` 65**5` , (ii) `2**135` , (iii) `6702**` , (iv) `91**67` , (v) `6678**1` , (vi) `835**86`

Answer

To solve the problem of replacing `**` with the smallest number to make the given numbers divisible by 9, we will follow these steps for each number:

### Step-by-Step Solution:

**(i) For the number `65**5`:**
1. Calculate the sum of the known digits: \( 6 + 5 + 5 = 16 \).
2. Let the missing digit be \( x \). The total sum becomes \( 16 + x \).
3. We need \( 16 + x \) to be divisible by 9. The nearest multiple of 9 greater than 16 is 18.
4. Set up the equation: \( 16 + x = 18 \) → \( x = 18 - 16 = 2 \).
5. Replace `**` with 2. The number becomes `6525`, which is divisible by 9.

**(ii) For the number `2**135`:**
1. Calculate the sum of the known digits: \( 2 + 1 + 3 + 5 = 11 \).
2. Let the missing digit be \( x \). The total sum becomes \( 11 + x \).
3. The nearest multiple of 9 greater than 11 is 18.
4. Set up the equation: \( 11 + x = 18 \) → \( x = 18 - 11 = 7 \).
5. Replace `**` with 7. The number becomes `27135`, which is divisible by 9.

**(iii) For the number `6702**`:**
1. Calculate the sum of the known digits: \( 6 + 7 + 0 + 2 = 15 \).
2. Let the missing digit be \( x \). The total sum becomes \( 15 + x \).
3. The nearest multiple of 9 greater than 15 is 18.
4. Set up the equation: \( 15 + x = 18 \) → \( x = 18 - 15 = 3 \).
5. Replace `**` with 3. The number becomes `67023`, which is divisible by 9.

**(iv) For the number `91**67`:**
1. Calculate the sum of the known digits: \( 9 + 1 + 6 + 7 = 23 \).
2. Let the missing digit be \( x \). The total sum becomes \( 23 + x \).
3. The nearest multiple of 9 greater than 23 is 27.
4. Set up the equation: \( 23 + x = 27 \) → \( x = 27 - 23 = 4 \).
5. Replace `**` with 4. The number becomes `91467`, which is divisible by 9.

**(v) For the number `6678**1`:**
1. Calculate the sum of the known digits: \( 6 + 6 + 7 + 8 + 1 = 28 \).
2. Let the missing digit be \( x \). The total sum becomes \( 28 + x \).
3. The nearest multiple of 9 greater than 28 is 36.
4. Set up the equation: \( 28 + x = 36 \) → \( x = 36 - 28 = 8 \).
5. Replace `**` with 8. The number becomes `667881`, which is divisible by 9.

**(vi) For the number `835**86`:**
1. Calculate the sum of the known digits: \( 8 + 3 + 5 + 8 + 6 = 30 \).
2. Let the missing digit be \( x \). The total sum becomes \( 30 + x \).
3. The nearest multiple of 9 greater than 30 is 36.
4. Set up the equation: \( 30 + x = 36 \) → \( x = 36 - 30 = 6 \).
5. Replace `**` with 6. The number becomes `835686`, which is divisible by 9.

### Final Answers:
- (i) `6525`
- (ii) `27135`
- (iii) `67023`
- (iv) `91467`
- (v) `667881`
- (vi) `835686`