The correct answer to the question is option 1: the Governor General. After India gained independence from British rule in 1947, the country transitioned into a parliamentary democracy. The role of the Governor General was similar to that of a constitutional monarch, with limited powers and largely ceremonial duties.

In this context, it was the Governor General who appointed the first Prime Minister of India. The first Prime Minister, Jawaharlal Nehru, was chosen by Lord Mountbatten, who was the last Governor General of India. Nehru`s appointment as Prime Minister was based on his leadership role in the Indian National Congress party and his broad support among the political leaders at the time.

The other options provided in the question are not correct. The President of India, as a constitutional head of state, has no role in appointing the Prime Minister. Mahatma Gandhi, although a significant leader in the Indian independence movement, did not have the authority to appoint the Prime Minister. Additionally, there was no committee headed by Dr. Rajendra Prasad involved in the appointment.

Therefore, the Governor General, as the representative of the British government during the transition of power, had the authority to appoint the first Prime Minister of India in 1947.