Explanation:

The correct answer is option 'A' (a).

In the given sentence, the phrase "a year ago" indicates an unspecified or non-specific time in the past. When referring to an unspecified time, we use the indefinite article 'a' before the noun.

Usage of Articles:

Articles are used to modify and specify nouns. There are three types of articles: definite article ('the'), indefinite article ('a' or 'an'), and zero article (no article).

1. Definite Article ('the'): It is used when we are referring to a specific or particular noun. It is used in the following cases:
- When the noun has already been mentioned or is known to both the speaker and the listener.
- When there is only one of that thing (unique or specific).
- When the noun is specific because it is a part of a limited group.

2. Indefinite Article ('a' or 'an'): It is used when we are referring to a non-specific or general noun. It is used in the following cases:
- When we mention something for the first time.
- When we are referring to any member of a group or category.
- When the noun is countable and not previously mentioned.

3. Zero Article (no article): It is used when we are referring to a general or abstract noun. It is used in the following cases:
- When talking about things in general or making general statements.
- When referring to plural and uncountable nouns in a general sense.

Application to the Given Sentence:

In the given sentence, "I first met him a year ago," we are referring to a non-specific or general time in the past. The phrase "a year ago" does not refer to a specific or known time. Therefore, we use the indefinite article 'a' before the noun 'year.'

Conclusion:

Hence, the correct article to use in the blank is 'a.' The sentence would be: "I first met him a year ago."