The correct answer is option 'C' - Lord Mountbatten.

Explanation:
After India gained independence from British rule on August 15, 1947, the country transitioned into a sovereign nation. As part of this transition, the position of Governor General was replaced by that of President. However, for a brief period of time between independence and the adoption of the new Constitution in 1950, the office of Governor General continued to exist.

Here is a detailed explanation of the options given:

a) C Rajagopalachari:
C Rajagopalachari, popularly known as Rajaji, was a prominent Indian political leader and a close associate of Mahatma Gandhi. He served as the first and only Indian Governor General of India from June 1948 to January 1950. However, he assumed office after Lord Mountbatten.

b) Jawaharlal Nehru:
Jawaharlal Nehru was the first Prime Minister of India after independence. He played a crucial role in shaping the country's policies and guiding it through the early years of nation-building. However, he did not hold the position of Governor General.

c) Lord Mountbatten:
Lord Mountbatten, formally known as Louis Mountbatten, was the last British Governor General of India. He served in this position from August 1947 to June 1948. He played a significant role in the partition of India and the creation of Pakistan. Lord Mountbatten was responsible for overseeing the transfer of power from British rule to an independent India. He worked closely with Indian leaders such as Jawaharlal Nehru and Mohandas Gandhi during this period.

d) Rajendra Prasad:
Rajendra Prasad was the first President of India. He assumed office on January 26, 1950, after the adoption of the Indian Constitution. He played a crucial role in the drafting of the Constitution and was elected as the President by the Constituent Assembly.

In conclusion, the first Governor General of India after independence was Lord Mountbatten. He held this position from August 1947 to June 1948, before being succeeded by C Rajagopalachari.