The exams are not an excuse for a women to uncover her face
Q: I am a female student in the second year of medical college in Cairo. I am an emigrant and my family lives in a town far away from me.
Last year Allah graced me with putting on Niqab (face veil). Then incidents (Part No. 17; Page No. 269
Shar`y (Islamic legal) proofs signify that it is impermissible for women to uncover their faces in the presence of their non-Mahrams except in cases of necessity. However, performing the exams is not a necessity that allows a woman to uncover her face in the presence of non-Mahrams. The foregoing is our view and Allah knows best.
Do your best to advise your father and explain the truth to him with wisdom and good preaching. Moreover, you have to be patient with the difficulties that you face for sticking to your Din and for calling your father and others to the way of Allah. We pray that Allah keeps you firm on following the truth and that He guides your father to it for He is the All-Hearer, the Responsive. He (Glorified be He) says:
And whoever holds firmly to Allâh, (i.e. follows Islâm - Allâh’s Religion, and obeys all that Allâh has ordered, practically), then he is indeed guided to the Right Path.
And whosoever fears Allâh and keeps his duty to Him, He will make a way for him to get out (from every difficulty).
And He will provide him from (sources) he never could imagine.
If there is a need to move legal guardianship from the nearest Waliy (a legally accountable person acting for a woman regarding marriage) to the one next, this should be referred to the Legal Court.
All what you have mentioned regarding your abidance by Shar`y Hijab, your disinclination to travel without being accompanied by a Mahram, your making of Shar`y Du`a'-ul-Istikharah, your Du`a' (Part No. 17; Page No. 274) that Allah may guide you to goodness is the undoubted truth. May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.