India

The chances of getting IIMC, Delhi are extremely less. It will be better if you opt for the same option and proceed with the admission.

Hello Rahul,
You may refer the link below for the list of top distance MBA colleges in India:
https://www.shiksha.com/mba/articles/top-10-institutes-for-distance-correspondence-mba-blogId-6301

Check out the link below and it has been ranked at 72 position:
http://www.dypcoeakurdi.ac.in/about-us/news-and-media/item/23-dy-patil-college-of-engineering-akurdi-has-ranked-72t-position-in-the-category-of-top-100-engineering-colleges

I can help you out with the name of top colleges in India for B.P.Ed. You can decide which one will be best for you.
1) Guru Nanak Dev University, [GNDU] Amritsar
2) Amity University, Noida
3) University of Delhi [DU], New Delhi
4) Bundelkhand University, Jhansi
5) Devi Ahilya Bai University, Indore.

There are no colleges that provide BA in one year. It is a graduation course, which requires minimum 3-years.

Sports Management is a relatively new concept in India taught in very few institutes across the country.
Top colleges offering this course are:
1) Alagappa University - Tamil Nadu
2) Indira Gandhi Institute of Physical Education and Sports Science - New Delhi
3) Institute of Social Welfare and Business