Yes definitely after completion of Graduation in Electronics and Communication Engineering applicants are
eligible to pursue Mass Communication and Journalism course .

The basic eligibility criterion for pursuing e is having graduation degree in any stream from any of the recognized university / college of the country.

Few Mass Communication and Journalism courses are given below :

Master in Communication Studies (MCS)
Master in Development Journalism & Electronic Communication
Master in Journalism and Mass Communication
Master in Mass Communication & Multimedia Production
Master in Mass Communication (MMC) + Post Graduate Diploma in Mass communication (PGDMC)
Master of Arts in Advertising & Public Relations
Master of Arts in Advertising and Design
Master of Arts in Advertising and Marketing Management
Master of Arts in Audio Visual Communication
Master of Arts in Broadcast Journalism
Master of Arts in Communication
Master of Arts in Communication, Culture & Media
Master of Arts in Convergent Journalism
Master of Arts in Hindi and journalism
Master of Arts in Journalism
Master of Arts in Journalism and Mass Communication (MAJM \ MAJMC)
Master of Arts in Mass Communication
Master of Arts in Mass Communication & Journalism
Master of Arts in Media and Communication
Master of Arts in Media Studies and Production
Master of Arts in Photojournalism
Master of Arts in Public Relations
Master of Arts in Vyavasayic Hindi(Patrakarita evam Jansanchar)
Master of Business Administration in Public Relations
Master of Mass Communication
Master of Mass Communication (M.M.C.)
Master of Mass Media
Master of Philosophy in Journalism and Mass Communication
Master of Science in Mass Communication
Master of Science in Mass Communication, Advertising and Journalism
Master of Science in Visual Communication
Master of Technology in Advanced Communication Systems

List of few colleges are given below :

Xavier Institute of Communications
Asian College of Journalism
AJ Kidwai MCRC Jamia Millia Islamia
Indian Institute of Mass Communication (IIMS)
Symbiosis Institute of Mass Communication
Indian Institute of Journalism & New Media
Mudra Institute of communications
Manorama School of Communication
Film and Television Institute of India
Times School of Journalism
Bharatiya Vidya Bhavan, Delhi
Amity School of Journalism And Communication, New Delhi
National Institute of Design (NID)
Journalism And Mass Communication – Mysore
Jagran institute of Management and Mass Communication (JIMMC)
National Institute of Mass Communication
International School of Media and Entertainment Studies
The Delhi School of Communication
Aizaz Rizvi College of Journalism and Mass Communication