If ∗ is a digit such that 7235∗ is divisible by 11, then the value of ∗ is:

A number is divisible by 11 if the difference between the sum of digits at odd places and the sum of digits at even places is either 0 or a multiple of 11.
Let the missing digit ∗ be x.
The number is 7235x.

Sum of digits at odd places (from right to left or left to right consistently):

Odd places from left (1st, 3rd, 5th)=7+3+x=10+x
Sum of digits at even places (2nd, 4th):

Even places from left=2+5=7
Difference between the sums:

Difference=(10+x)−7=3+x
For the number to be divisible by 11, this difference must be 0 or a multiple of 11 (such as 11,22,…).
Since x is a single-digit positive integer (0≤x≤9):

3+x=11
x=11−3=8