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There cannot be a standard rule for including/excluding a preposition. You have to read the sentence and ensure that it still makes sense with/without the given preposition, or whether the preposition is already provided out of bracket. Generally, removing the preposition from a noun term will result in a grammatical error.
So, typically, yes. We have to use prepositions in sentence completion questions, but in the case of other type of questions, (sometimes) it may not be required.