4. Did she studied philosophy at university?

The correct sentence is: Did she study philosophy at university?

Explanation: The auxiliary verb 'Did' is used for past simple questions. When 'Did' is used, the main verb should be in its base form (not past tense). 'Studied' is the past tense of 'study,' but after 'Did,' we should use 'study.' So, 'Did she study...' is the correct form.