Explanation:

- The sentence "He asked whether either of the brothers ___________" suggests a singular subject because "either" refers to one of the two brothers.

- Option 1: "were at home" - Incorrect. "Were" is plural and doesn't match with the singular subject "either."

- Option 2: "are at home" - Incorrect. "Are" is plural and doesn't align with "either," which requires a singular form.

- Option 3: "was at home" - Correct. "Was" is singular and matches with "either," indicating one of the brothers being at home.

- Option 4: "have come home" - Incorrect. "Have" is plural, not compatible with the singular form expected here.