Distance

Yes, the universities which are approved by UGC & DEB are good to pursue your MBA but currently the issue is that SMU is having approval of DEB till 2017 only. So, the students those who are completing their MBA in 2017 will be considered as a valid student. Also, SMU does not have its information offices to provide services as well as information to their students.
May I know your current location and your last qualification as well as your interest for the specialization?

You are eligible for appearing in CAT to seek admission in MBA provided your university is recognised and you complete B.Tech with greater than 50% marks.

You may refer to following article for list of top 10 best universities for MBA by distance learning:
https://www.shiksha.com/mba/articles/top-10-institutes-for-distance-correspondence-mba-blogId-6301.
You may prefer any of these 10 universities over Bharathiar University.

Yes, you can complete your graduation through distance learning from IGNOU and there are many more universities as well who offer distant learning.
Distance learning courses are getting popular in India and a lot of students want to earn their degree while working.
Click on this link to know the list of universities:
http://www.indiaeduinfo.com/cores/ba.htm

You can prefer the courses from Indian Institute of Hotel management at Delhi.

You should prefer IGNOU-Delhi, Bharatiya Vidya Bhavan,-Delhi, IMT-Ghaziabad, etc.

NMIMS is obviously the best institute in implementation of the course, and other evaluation method. Prefer NMIMS first and then IMT.