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Astronomers at the Palomar Observatory have discovered a distant supernova explosion, one that they believe is a type previously unknown to science`
A that they believe is one restricts supernova explosion. that is redundant because it is also restrcits the sentence.
B that they believe it to be one restricts supernova explosion. that is redundant because it is also restrcits the sentence.
C they believe that it is of b]one[/b] acts as a pronoun to restrict the clause. we do not need to restrict the sentence twice with that. it refers back to the explosion. We cannot have two pronouns referring back to the same noun.
D they believe that is tricky one here. believe needs that to make sense. however, they believe that is a type previously unknown to science does not make sense. a type cannot be unknown to science. we need the preposition of.
E they believe to be of Correct. Idiom: believe X to be Y.