In the quiz it was expected that you choose this form as well as the expected J'ai reussi mon exam or J'ai obtenu mon exam. In the lesson it states that you can use J'ai eu with the name of the exam (e.g. bac or licence).
So would a French speaker really use the J'ai eu or J'ai obtenu form with "mon exam"?
It seems unlikely. Rather like in English we would not say "I got my exam" or "I obtained my exam" where, of course, we have no problem with "I got my degree" or "I obtained my dregree"