The British Governor General and Viceroy who served for the longest period in India was

The British Governor General and Viceroy who served for the longest period in India was Lord Dalhousie. He held the position from 1848 to 1856, which amounts to a total of 8 years. During his tenure, Lord Dalhousie implemented various significant policies and reforms, including the Doctrine of Lapse and the construction of railways.

Option A: Lord Irwin served as Viceroy from 1926 to 1931.
Option C: Lord Curzon served as Viceroy from 1899 to 1905.
Option D: Lord Linlithgow served as Viceroy from 1936 to 1943, which is a period of 7 years.

Therefore, the correct option is Option B: Lord Dalhousie, who served for the longest period of 8 years as Governor-General of India.