The answer could only be E; it is the only answer that’s both grammatically and logically correct. In the sentence in E, the pronoun “he” is properly supplied as the doer of the action of conducting the orchestra, and the past participle “had conducted” is the correct tense for the repeated action in the indefinite past. The sentence works properly as a whole because both the main clause and the subordinate phrase are properly constructed and linked by the subordinating conjunction “after.”
It couldn’t be B because the pronoun “his” in the subordinate phrase “after his conducting the orchestra for six concerts’ doesn’t have a proper antecedent or referent noun. That antecedent or referent noun should be a musical conductor, but nowhere in the sentence is there any reference to that person. The possessive “Beethoven’s Ninth Symphony,” which might seem to be the antecedent or referent noun, actually doesn’t qualify because it is not a person but an inanimate object.
A and C are wrong answers because each of them doesn’t have a referent noun doing the action; for the same reason already given above, the noun form “Beethoven’s Ninth Symphony” doesn’t qualify as that referent noun, being an inanimate object.
D is a wrong answer because its subordinating conjunction, “although,” is illogical and inappropriate to the statement.
