The digit by which '*' should be replaced in 7254*98 so that the number formed is divisible by 22 is

1. 0

2. 1

3. 2

4. 6

22 = 2 × 11, and 2, 11 are co-prime. So the number must be divisible by both 2 and 11.

Last digit is 8, so divisible by 2 for any value of *.

For divisibility by 11:

Digits from right: 8, 9, *, 4, 5, 2, 7.

Sum of digits at odd places (from right) = 8 + * + 5 + 7 = 20 + *.

Sum of digits at even places (from right) = 9 + 4 + 2 = 15.

Difference = (20 + *) − 15 = 5 + *.

For divisibility by 11: 5 + * = 11 ⇒ * = 6.

Hence, option 4 is the correct option.