Explanation:

- Statement I: Karnataka is the largest producer of coffee in India.

- Correct. Karnataka is indeed India's largest coffee-producing state.

- Statement II: Arabica is a variety of coffee.

- Correct. Arabica is a well-known variety of coffee, known for its flavor and aroma.

- Statement III: The Arabica variety initially brought from Mexico is produced in India.

- Incorrect. Arabica coffee was originally brought to India from Yemen, not Mexico.

- Option 1: I, II and III.

- Incorrect. Statement III is false.

- Option 2: Only II and III.

- Incorrect. Statement III is false.

- Option 3: Only III.

- Incorrect. Statement III is false.

- Option 4: Only I and II.

- Correct. Both statements I and II are correct.

Correct Answer: Option 4 - Only I and II.