Often said to be the most perfectly cut of all large diamond

A,B & E have dangling modifiers. "The Jubilee's facets" is not a diamond. Between C & D, C wins for concision and hence is the right answer. IMO, D is also gramatically correct.

Well "C" has "it" twice making its reference very unclear.

Unclear as in?.. What other noun could "it" be referring to?

I don't think so.

C says 'it can be balanced'. Here 'balance' is not an action that is done by the subject 'it'. Here the action 'balance' is happening upon the subject. Hence, passive voice is correct.
D says 'it can balance'. The subject of the verb 'balance' is the pronoun'it' referring to the diamond. A diamond cannot balance itself, it has to be balanced by something.

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Often said to be the most perfectly cut of all large diamonds, the Jubilee’s facets are so exact that it can be balanced on its culet, which is less than two millimeters across.

In the question stem the modifier highlighted in red modifies the facets of The jubliee and not the jubliee itself; It must modify the jubliee.So option A,B,E are starightway gone.Between C and D, D has a logical error as it tries to convince that the diamond can balance itself on its cutlet,so answer must be C.

A. the Jubilee’s facets are so exact that it can be balanced on its culet, which is less
B. the Jubilee’s facets are so exact that the diamond can be balanced on its culet, less
C. the Jubilee has facets so exact that it can be balanced on its culet, which is less
D. the Jubilee has facets which are so exact that it can balance on its culet, which is less
E. the Jubilee’s facets are so exact that it can be balanced on its culet, which is lesser

C. the Jubilee has facets so exact that it can be balanced on its culet, which is less

I think here "it" can refer to "facets" as well. so there is ambiguity here. Please correct where i am wrong.

Singular pronoun cannot refer to plural noun.

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