The state's definition is given in which article of Indian Constitution?

The definition of "State" in the context of the Indian Constitution is given in Article 12.  Article 12 defines "the State" for the purposes of Part III of the Constitution, which deals with Fundamental Rights. According to Article 12, "the State" includes the Government and Parliament of India, the Government and the Legislature of each of the States, and all local or other authorities within the territory of India or under the control of the Government of India.