Problems in building model predicting probablity of student's admission
Make sure you model the $Y$ data in the correct way.

Some reasons I can think on why do you have such strange results:


You are modelling binary Yes/No answers for all the students vs all the faculties, make sure you only take into account students which presented to the given faculty (some of them passed and some didn't), not all the students.
Sometimes more exams add noise to your answer, because the faculties look for specialized individuals who outperformed in what they are looking for, and that means you will find that the other results are "noise" for the answer.