At the time of the partition of India, the President of the Indian National Congress was Acharya J.B Kriplani.

Option 1: Pandit Jawaharlal Nehru was not the President of the Indian National Congress during the time of partition. However, he did become the first Prime Minister of India after independence.

Option 2: Sardar Vallabhbhai Patel was an important leader during the Indian independence movement, but he did not serve as the President of the Indian National Congress during the partition.

Option 3: Maulana Abul Kalam Azad, a prominent freedom fighter, was the President of the Indian National Congress from 1940 to 1945. However, he did not hold the position during the partition of India.

Option 4: This is the correct answer. Acharya J.B Kriplani was the President of the Indian National Congress during the time when India was partitioned into India and Pakistan in 1947. He served as the President from 1946 to 1947.

In conclusion, the correct answer is option 4, Acharya J.B Kriplani.