Explanation

Though implies that the matters about which a professor enjoys liberty are opposite those “irrelevant to his subject.” So you might anticipate an answer like “relevant.”

Germane and pertinent are the best synonyms. Mimetic and congruent are slightly related to the idea at hand — the former means “copying” (like a mime, for instance) and the latter means something like “standing in a similar relation.”

Hence options germane, pertinent are best fit!