India

Ace Engineering Academy and Made Easy are renowned coaching classes for GATE. Still, I would suggest before taking admission any one of them, at least check out the notes from the both coaching classes and meet some students who already had completed their classes. I had attended ACE-Hyderabad I can tell you that they have very good notes and teaching faculty.

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.