Democritus’s theory (.............) is similar to modern atomic theory.
What exists in the highlighted portion is a clause that modifies Democritus's theory.
(A) OF THERE BEING A SET OF INDIVISIBLE PARTICLES MAKING UP ALL MATTER BEARS A STRIKING RESEMBLANCE TO MODERN ATOMIC THEORY - Plug this answer choice back to the question and this is what you get: Democritus's theory of there being..... - this is super awkward. Moreover, the entire option (A) becomes a part of the prepositional clause commanded by the subject 'democritus's theory'. So, the structure of the sentence now effectively becomes [Noun] [Prepositional phrase]. So, under this structure, the meaning of the sentence changes completely. Now, there is no comparison involved. But based on the initial reading of the passage, democritus's theory is being compared to modern atomic theory. Hence, (A) is incorrect. So, eliminate (A)
(B) OF A SET OF INDIVISIBLE PARTICLES THAT MAKES UP ALL MATTER BEARS A STRIKING RESEMBLANCE TO MODERN ATOMIC THEORY - (B) is incorrect for the same reasons mentioned in (A). So, eliminate (B)
(C) THAT A SET OF INDIVISIBLE PARTICLES MAKES UP ALL MATTER BEARS A STRIKING RESEMBLANCE TO MODERN ATOMIC THEORY - Option (C) is a neat relative clause modifier that clearly modifies democritus's theory. Also notice that there's a neat comparison between democritus's theory and modern atomic theory. Hence, (C) is the correct answer.
(D) WHICH IS THAT THERE IS A SET OF INDIVISIBLE PARTICLES MAKING UP ALL MATTER BEARS A STRIKING RESEMBLANCE TO MODERN ATOMIC THEORY - this is also a relative clause but the difference here is that "which clauses" have to be separated from the noun it tries to modify by a comma. Since there is no comma here, (D) is wrong.
(E) WHICH BEARS A STRIKING RESEMBLANCE TO MODERN ATOMIC THEORY IS THAT THERE IS A SET OF INDIVISIBLE PARTICLES MAKING UP ALL MATTER - (E) is WRONG for the same reason mention in the explanation for (D).