Roy, I explained this question in our video. If necessary, you should watch it again.
Basic knowledge 1: Idiom - believe (you can find this in our handout)
(1) believe in sb
(2) believe + that (object clause)
(3) believe sth to be
believe + double objects such as believe sth sth, believe sth that (object clause) is wrong
Basic knowledge 2: attributive clause
Example: This is a movie I like.
This is a correct sentence. “I like” is the attributive clause in this sentence.
This sentence is composed of 2 simple sentences:
This is a movie. I like the movie.
Then, combined as “This is a movie that I like” where the word “that” refers to “movie”
In formal written English, when “that” serves as object in the attributive clause, such as the example above, we MUST omit it. Therefore, we come up with our final sentence: This is a movie I like.
Similarly for Choice E
, one they believe to be of a type
"they believe to be of a type…" is the attributive clause used to modify “one”=explosion.
So before omitting "that"
it is like the following:
“one that they believe to be of a type…” where “that” serves as the object of “believe” - even it is omitted but it is still there!
Thus, if you put the attributive clause back to simple sentence it is:
they believe that (=one=explosion) to be of a type - right idiom.
Similarly, you can analyze why the other choices are wrong.