The correct answer to the question is option 3, Lord Mountbatten. Lord Mountbatten served as the first Governor-General of Independent India from 1947 to 1948.

Option 1, C. Rajagopalachari, was the last and only Indian Governor-General of India, but not the first. He took office in 1948, succeeding Lord Mountbatten.

Option 2, Rajendra Prasad, was the first President of India, not the first Governor-General. He assumed office in 1950, after the adoption of the Indian Constitution and the transition to a republic.

Option 4, S. Radhakrishnan, was the second President of India, not the Governor-General. He served as President from 1962 to 1967.

In summary, Lord Mountbatten was the first Governor-General of Independent India, serving from 1947 to 1948.