There are many Universities offer the programme, The universities conduct their own entrance exam. Here are some of the Government Institute for the programme you can prefer:

Jamia Millia Islamia- BA in Mass Media Hindia

Delhi College of Arts and Commerce- BA (Hons.) Journalism

KC College of Arts, Science and Commerce, University of Mumbai- Bachelor of Mass Media (BMM)

Madaras Christian College- B.A. Journalism

You can also check the entrance & other top colleges with the given below link.

https://media.careers360.com/articles/top-mass-communication-entrance-exams-in-india

Good Luck!