Under which Article of the Constitution is the President's rule promulgated in any state in India?

Correct option is D

President's rule under Article 356 of the Indian Constitution can be imposed in any state of India. According to this article, if the government of a state is unable to govern the state as per the constitutional provisions, the central government can dismiss the government of that state and take over the administration of the state.

It is initially imposed for 6 months.
It can be extended up to a maximum of 3 years (with the approval of the Lok Sabha).
This article was first invoked in the history of India in 1951, in Punjab.

Article 326: Right to vote in elections. (Determines eligibility to vote)
​Article 370: Article granting special status to Jammu and Kashmir (mostly repealed in 2019).
Article 352: Provision for declaring a national emergency. This is invoked when the sovereignty, integrity, or security of the country is threatened.