The correct answer is option 3, the Government of India Act of 1935. This act was a significant step towards introducing a federal form of government in India.

Option 1, the Government of India Act of 1919, did introduce certain elements of self-government and provincial autonomy, but it did not establish a federal system at the center.

Option 2, the Indian Councils Act of 1909, was another step towards limited self-government, but it also did not introduce a federal structure.

Option 4, the Indian Independence Act of 1947, was the legislation that granted India independence from British rule, but it did not specifically introduce a federal form of government.

Therefore, the Government of India Act of 1935 is the correct answer as it was the act that formally introduced a federal system at the center in India.