Distance

Yes, there are many university which providing Master and PhD level program in distance or part-time mode. You may visit the website of Indra Gandhi Open University for eligibility criteria in your field of studies.

For distance learning programme, there is no compulsion of graduation percentage. So accordingly, you can apply of the universities for MBA distance programme.

Annamalai University Distance Education MBA 2017: Like many other distance education courses, Annamalai University, Tamilnadu, also offers one general & 5 other specialized MBA programmes under distance education.
To be eligible for the MBA courses offered by the university, any Degree (except 10+2+2 pattern) or an equivalent examination is required.
Admission to all the distance education MBA courses offered by Annamalai University is available in 2 ways. I.e
Spot Admissions.

Part-time course is the one in which one has to attend classes either in evening or on weekends as per the schedule by the course provider and in one correspondence course there is no classes, if any query is there it can be solved online or you can go for the same to the study center.

Try for Symbiosis or even GJU, Hisar can be a good option. Distance learning depends on the material rather than the name of a university.

Yes, you are eligible to seek admission in MCA after B.Com as you had maths as a subject in 10+2 stage.

IIT-Delhi is the best. DTU and NSIT are after it.