An appositive is a noun or a pronoun that is close to another noun or pronoun to identify that word or to give more information about it. They can either be essential or nonessential. The first ones are required to the meaning of the sentence, to make it clear. They are not set off with commas. On the contrary, nonessential appositives add information which is already clear. They are set off with commas.
Taking all this into account, your answers would be the following ones:
1) b
2)b
3)a
4) a
A test you can apply in order to identify whether the appositive is essential or not is to remove it from the sentence. If you do so and the sentence still makes sense and is still grammatically correct, then the appositive is non-essential.
1. Ashe's first title was in 1965
2. The Keystone Cops debuted in 1912
3. This trip took ten days
4. *Presidential candidate had just won the election
As you can see, sentence 3 is still grammatically correct without the appositive but in that example A is the one okay because the other one (b) is wrongly punctuated. Sentence 4 is a clear example of an appositive which adds important information for the sentence's meaning to be clear. If you dropped it, you would not know which president you are talking about.
