The correct answer is (a) James Outram.
James Outram was the British Resident in Avadh at the time of its annexation into British Dominion. He was a British soldier and statesman who served in India for over 30 years. He was known for his military prowess and his administrative skills. He was also a strong advocate for the rights of the Indian people.
W.H. Sleeman was a British officer who served in India. He is best known for his work in suppressing the Thuggee cult. He was also a writer and a historian.
Bishop R. Heber was an Anglican bishop who served in India. He was a prolific writer and a keen observer of Indian culture.
General Low was a British general who served in India. He is best known for his role in the First Anglo-Maratha War.
Outram was the most likely of the four to have been the British Resident in Avadh at the time of its annexation into British Dominion. He was a senior British official who had served in India for many years. He was also a strong advocate for the annexation of Avadh.