The answer is letter D. Neither beauty nor popularity was considered in the contest.
Explanation:
Correlative conjunctions are used in pairs:
both ... and
either ... or
neither ... nor
not only ... but also
not ... but
Their function is to correlate words or phrases that have the same importance in a sentence.
Since the correct pairing is "neither ... nor", the only correct option is letter D. "Neither ... nor" gives a negative meaning to both the words or phrases they accompany. In the sentence we are studying here, beauty was not considered in the contest. Popularity was also not considered in the contest.