Examination again

Since no two students have given the same sequence of answers, the number of students is less than or equal to the number of possible sequences = $2^10 = 1024$

If $n \le 1024$ is the total number of students, then the number of passed students = $\frac{8}{11}n$ .

For the number of passed students to be an integer (and be maximum), $n$ should chosen as the number divisible by 11 and less than 1024. This gives $n = 1023$

and passed students = $\frac{8}{11}1023 = \boxed{744}$