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The correct answer is option 4, Mountbatten. India became independent from British rule on August 15, 1947, under the viceroyalty of Lord Mountbatten. Lord Mountbatten served as the last viceroy of British India from March 1947 until India`s independence. He played a crucial role in the transfer of power from British rule to Indian hands.
Option 1, William Bentinck, is incorrect because he served as the Governor-General of India from 1828 to 1835, which was much earlier than India`s independence.
Option 2, Wellesley, is also incorrect because Richard Wellesley served as the Governor-General of India from 1798 to 1805, again much before India`s independence.
Option 3, Wavell, is incorrect because Archibald Wavell served as the Viceroy of India from 1943 to 1947, but he was not the viceroy during India`s independence.
Therefore, the correct answer is option 4, Mountbatten.