Which 'Article' gave the centre the powers to take over a state administration on the recommendation of the governor?

Article 356

The correct answer is Option (2) → Article 356

Article 356 gave the Centre the powers to take over a state administration on the recommendation of the Governor

Article 356 of the Indian Constitution, also known as the "President's Rule," deals with the imposition of Central rule in a state. This article is titled "Provisions in case of failure of constitutional machinery in States." It empowers the President of India to assume control over the state's administration when the Governor of a state reports that the constitutional machinery in the state has broken down.
This may occur due to various reasons, including political instability, the failure of the state government to function in accordance with the Constitution, or other extraordinary circumstances.