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The correct answer for the governor-general during the Second Anglo-Mysore War is option 4, Warren Hastings. Lord Wellesley, option 1, served as the governor-general during the early 19th century and was known for his policy of aggressive expansion against the French and Indian powers. Lord Cornwallis, option 2, served as the governor-general in the late 18th century and is known for his administrative reforms in British India. Sir John Shore, option 3, served as the governor-general before Lord Wellesley and is known for his policy of non-intervention in Indian affairs. Therefore, option 4, Warren Hastings, is the correct answer as he served as the governor-general during the Second Anglo-Mysore War, which occurred in the late 18th century.