What is the ruling on sitting next to a female student during an examination, given that it is not possible to transfer to another school?

The basic principle is that the mixing of men and women is impermissible, due to the corrupting influences that result from it. However, for extreme necessity, it is permissible to study in mixed environments under certain conditions, including: lowering the gaze, avoiding seclusion (khalwa), not speaking with women except within the confines of the lesson, and avoiding temptation as much as possible. The rule is that what is forbidden as a means (to a haram end) may be permitted out of necessity. If a non-mixed school is available, then it is obligatory to enroll in it.