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Yes, you are eligible. Some of them are:
In Delhi/NCR: IIT Delhi DMS, International Management Institute (IMI), Institute of Management Studies (IMS), Lal Bahadur Shastri Institute of Management (LBSIM), NIILM Centre for Management Studies, IILM Institute for Higher Education, Apeejay School of Management, Fostiima Business School, Indian Institute of Finanace (IIF).
In Pune: indira Institute of Management- Pune (IIMP), Sinhgad Institute of Management, Symbiosis Center for Information Technology (SCIT), Balaji Institute of Management & Human Resource Development (BIMHRD).
In Mumbai: National Institute of Industrial Engineering (NITIE), Shailesh J Mehta School Of Management, IIT Mumbai(SJSOM), K.J. Somaiya Institute of Management Studies and Research (SIMSR), Welingkar Institute of Management (We School), Siescoms.
In Bangalore: Acharya Institute of Management and Sciences (AIMS), IFIM Business School, Alliance Business Academy.

Dear aspirant,
Glad to meet you.
fee structure for integrated BBA MBA course at NIRMA University :INR 291,800 (First Year Fees).
Total Fees - 18.79 Lakhs
NIRMA University Integrated MBA Course Highlights:
Nirma University charges a total fee of INR 1.16 Lacs for its integrated BBA+MBA course.
Number of Seats allocated for the course is 180
Opportunity to specialize in various management areas such as Marketing, Finance, Operations, Strategy, Human Resource Management, International Business, and Business Analytics during MBA.
Nirma University Integrated MBA Eligibility Criteria:
For All India Category:
Candidates should have passed Higher Secondary Certificate (HSC) Examination (10+2) or any other equivalent examination from the school located in India (including Gujarat State) and recognized by Nirma University, with a minimum 60% aggregate marks at first attempt.

Yes, it is a good decision to pursue mass communication.
Mass Communication courses broaden your horizons to the different types of careers one can pursue in the communication sector. Do remember that the constant emergence and evolution of media technology will see new jobs and specialities being created and other jobs being made irrelevant.
I would suggest figuring out what interests you the most while studying so that you can decide what you would like to specialise in. Do not be disheartened or biased towards any subject or topic you may encounter during your course as you may end up becoming fond of something that you did not particularly appreciate at the beginning :)
When you find out what you would really like to specialise in, you could try to work towards landing that internship and/or job of your dreams. After garnering some "real world" experiences you could go on to study a postgraduate course in your speciality to complement everything you've learnt.
That being said, you could be anything from a Public Relations executive, Marketing Executive, Community Manager/Social Media Manager, Media Planner, Advertising Accounts Executive/Manager, (if you are particularly creative) Graphic Designer, News/TV/Film/Radio Producer, Journalist, Editor, Cameraman, Speech Writer to a Political Spin Doctor.

DoMs-NIT, Trichy is situated in the NIT-Trichy main campus. It has all the possible amenities. The curriculum of DoMs-NIT, Trichy gives a lot of flexibility to the students. Hence, even if you are pursuing MBA, you can hope to do a plethora of other work like social work, entrepreneurship, etc. (part-time will not be possible though). Currently, we have people from all over India in class (from Tripura to Rajasthan and Himachal to Kerala), and that has proven to be one of the biggest learning experiences of my life. Also, everything happening at DoMs-NIT, Trichy is student based. We handle our guest lectures, alumni relationship, public relationship, admissions etc. on our own. Personally being in the guest students visitor, I have learnt a lot. The faculty is very friendly and supportive. DoMs-NIT, Trichy being a small close-knit community, we share a strong bond with everyone in it. At the end of the day, everything boils down to your capabilities. Average package is Rs 7-8 lakh for fresher.