Explanation:

- Statement I: Battle of Buxar - 1764

- This is correct. The Battle of Buxar occurred in 1764 between the British East India Company and the combined forces of Indian rulers.

- Statement II: Battle of Plassey - 1757

- This is also correct. The Battle of Plassey was fought in 1757 and marked a decisive victory for the British East India Company over the Nawab of Bengal.

- Option 1: Only I

- Incorrect, as both statements are correct.

- Option 2: Both I and II

- Correct. Both statements are correctly matched with their respective years.

- Option 3: Only II

- Incorrect, as both statements are correct.

- Option 4: Neither I nor II

- Incorrect, as both statements are correct.

The correct choice is:

Option 2: Both I and II