OPTION "A" is the correct answer.
EXPLANATION:
There are two types of articles:
DEFINITE ARTICLE (THE) : Article 'the' is used to refer to a DEFINITE thing or person.
INDEFINITE ARTICLE(A/AN): Article 'a/an' is used to refer to a thing or person in general. For instance: man, door etc.
Article 'a' is used with consonant sounds whereas article 'an' is used with vowel sounds.
In the FIRST Blank, article "the" will be used because article 'the' is used with superlatives.
Similarly, In the second blank, article "the" will be used because article "the" is used with superlatives.
In the third blank, "no article" will be used because the term 'college' doesn't need specification. It just refers to a place where the eldest boy is studying.