The correct option is B Exist at the core of nearly all galaxies and that the mass of each black hole is proportional to that of
The sentence as is has a few errors. First, each side of 'and' has a full independent clause- "scientist have recently found evidence that black holes exist at the core of nearly all galaxies.." and "...the mass of each black hole is proportional to its host galaxy". The major error here is that the second independent clause seems like a complete, separate statement. Additionally, without a 'that' at the beginning of this clause, it is unclear whether the scientists have found evidence to support it or not. Also, the use of 'to' in "the mass of each black hole is proportional to its host galaxy" is inappropriate as it seems to suggest the mass is proportional to galaxy itself and not to the MASS OF its host galaxy. While option A repeats all of the aforementioned errors, C repeats this last one. Option D has a subject-verb error- "scientists have found evidence that black holes..." and "exists" (plural subject followed by a singular verb). E has the same error. Option B, however, rectifies all these errors and does not create any more errors. Thus, B emerges as the correct answer.