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Vishwa Bharti University SANGIT BHAVANA (INSTITUTE OF MUSIC, DANCE & DRAMA) is offering the following courses.
1. UNDER-GRADUATE (Bachelors IN PERFORMING ARTS
2. Masters IN PERFORMING ARTS
3. M.Phil
4. Ph.D.
5. Certificate COURSE of two years duration
6. ONE-YEAR COURSE FOR FOREIGN STUDENTS
7. SHORT TERM COURSE ON ESRAJ
So from above Diploma in Dance is not available here. You can do the Certificate course of two years of duration. The eligibility criteria is given below.
1. Passed Madhyamik or equivalent examination,
2. Staff, Staff-ward and Students of Viva-Bharati,
3. Residents living within the radius of 8 Km of Viva-Bharati. For more details please visit Viva Bharati University website.

Yes, you can get into MA fine arts after completion of your BA degree.
Here I would like to suggest you choose Chandigarh University. Which is a fast-growing university with numerous placements.
You can find the admission details below,
CUCET 2021 Registrations Open.
CUCET is the entrance test for Chandigarh University.
Coming to the placements,
The placements at Chandigarh University are well-known. The placement cell performs admirably. The campus attracts a large number of reputable companies. As a result, the majority of students get placed. Around 70 to 80 percent of students, I believe, get placed in various firms. The typical annual compensation provided is in the range of 5 to 6 lakhs. The top-notch companies like Amazon, Apollo, BAJAJ Allianz, Dell, Deloitte, Genpact, Google, HCL, HP, ICICI Securities, just dial, L T, Microsoft, Motorola, Muthoot Fincorp, NIIT, Radisson, Samsung, Shoppers Stop, The Leela, Videocon, YesBank and etc. comes to recruit the students from the university.
I hope this info will help you out.
All the best.