The Indian Constitution was adopted on 26th November, 1949.

Option 1, 15th August, 1947, is the date when India gained independence from British rule, but it is not the date when the Indian Constitution was adopted.

Option 3, 26th January, 1950, is the date when the Indian Constitution came into effect and India became a Republic. It is not the date of adoption, but the date of implementation.

Option 4, 2nd October, 1952, is not relevant to the adoption of the Indian Constitution.

Therefore, the correct answer is option 2, 26th November, 1949. This is the date when the Constitution of India was officially adopted by the Constituent Assembly and signed by the members.