There is no any common entrance exam to get admission for Bachelor of Journalism and Mass Communications. There are University level exams which is conducted by the particular university. 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

If you specify the particular college to which you want to get the admission then I can help you for the syllabus if the college has entrance for the programme.

Good Luck!