Choose the sentence which has the appropriate use of Article/s:

The correct answer is Option (1) → Mathematics is an interesting subject.

Articles with names of subjects and with a/an:

• Names of subjects, games and meals used in a general sense take no article: Mathematics, tennis, lunch.
• A singular countable noun naming one of a kind takes a/an:
  • an before a vowel sound: an interesting subject;
  • a before a consonant sound: a useful subject.
• Many fixed phrases take no article: at hand, at home, by heart.
  Example: English is an easy language to learn.

Why the Other Options are Incorrect?

Option 2: The Tennis is not our national game. — Incorrect. Names of games take no article: "Tennis", not "The Tennis".
Corrected: Tennis is not our national game.

Option 3: I have had the lunch. — Incorrect. Names of meals in general take no article ("the lunch" only for a particular meal, as in "the lunch at the wedding").
Corrected: I have had lunch.

Option 4: Our examination is at the hand. — Incorrect. The fixed phrase is "at hand" (near in time), without an article.
Corrected: Our examination is at hand.