The correct answer is option 3: Resident. A Resident was a British Officer who represented the Governor General in a state that was not directly under British rule. The role of the Resident was to act as an advisor to the ruler of the state in matters related to the British government. They would oversee the political and administrative affairs of the state, with the aim of ensuring that the interests of the British East India Company were protected.

Option 1, Collector, refers to a different role. A Collector was a British officer responsible for collecting revenue and managing the administration of a district.

Option 2, Viceroy, is not the correct answer. The Viceroy was the highest-ranking British official in colonial India, serving as the representative of the British monarch and having authority over the entire country.

Option 4, Agent, is also not the correct answer. An Agent can refer to different roles, but in this context, it does not accurately describe the specific role of the British Officer in question.