Is it permissible for a student residing in a European country to shorten prayers if their studies occupy the entire day?

If you are residing in or near the college, you are not permitted to shorten your prayers (qasr). However, if you are residing at a distance that allows for qasr, then it is permissible for you to do so. The permissibility of traveling to non-Muslim countries for study is conditioned upon the unavailability of such studies in Muslim countries, and the existence of a genuine need for them. Otherwise, traveling is not permissible, and consequently, shortening prayers is also not permissible.