OE

Split #1: This subject is a neither P nor Q structure. Whether the first term, P, is singular or plural does not matter at all. All that matter is the second term, Q, which here is “Beethoven, as well as Schubert in the early 19th century.” Of course, the “as well as” is an additive phrase, so does not count as part of the subject. The only relevant subject is “Beethoven,” and of course Mr. Beethoven is singular. We need the singular verb. Choices (A) & (B) & (C) are all incorrect.

Split #2: to describe a single activity, the correct idioms is “known to compose”: these people did not do this one thing, composing suites, but that is not what made them famous overall. The idiom “known for composing” is a correct idiom, but here it illogically implies that not composing suites is precisely what made these men famous: that’s ridiculous! The construction “known by composing” even more illogically suggests that someone else, unnamed, does the composing, or the “not composing”, and this is how we know these men. The construction “known in composing” is not a correct idiom at all. Only (A) and (D) use the correct idiom for this context.

Choice (D) is the only possible answer.
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Mahmud6
At 4.12 PM, you gave the problem and then at 4.13 PM, you gave the OA and OE also. What is the hurry? Where is the opportunity for a discussion?
My humble suggestion to you is to wait for a few postings before you reveal the OA or OE.
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Neither the late 18th century composers, such as Mozart or Haydn, nor Beethoven, as well as Schubert in the early 19th century, were known to compose in the suite format, so popular in the Baroque period.

(A) were known to compose
(B) were known in composing
(C) were known for composing
(D) was known to compose
(E) was known by composing

Straight D
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The idiom here is "neither x nor y" and the simple rule of thumb is that the person ( singular or plural) of the verb that comes after y is determined by the person of y. So if "y" is a singular noun or pronoun then a singular verb must follow and if "Y" is a plural noun or pronoun then a plural verb must follow.

D

A real good question with good trap doors. The idiom "Neither....nor..." will always have a subject verb agreement as per the singularity or plurality of the word that follows "nor".
Here Beethoven is that word which is singular (mind the "as well as" s-v rule). Hence we can eliminate A, B & C.
Between D and E, "by composing" has a lot of issues. "To compose" is prefered.

Hence Option D.