Is it permissible for a university student studying in hospitals to submit undressed photographs for an admission card to a hospital that is considered technically superior and offers the best training, with her intention to wear the hijab inside the hospital and conceal the photographs after submission?

The hijab is an obligation upon the Muslim woman, and it is not permissible for her to reveal her allurements in front of non-mahram men, whether directly or through photographs. The basic principle is that it is not permissible to study or train in a hospital that requires immodest appearance in a photograph, unless abandoning the study would lead to a greater harm, such as the unavailability of a Muslim female doctor to treat women, which would result in non-mahram men seeing their private parts. In this case, it is permissible, because providing a Muslim female doctor is a communal obligation (fard kifaya), and committing the lesser of two evils (the appearance of the picture) to avert the greater evil (men seeing private parts) is permissible in Islamic law.