Distance/Correspondence MBA

https://www.shiksha.com/university/nmims-university-Mumbai-52743
You will find all the true and authentic information about your college here.

You can do the corresponding MBA from Delhi University or IGNOU.

You can explore about the following-
Narsee Monjee
Amity corporate solutions
MATS university
XIBMS
St. Xavier's college
Makaut
Calcutta university.

Yes, you can pursue a regular and correpsondence degree together from different Universities in India. I will suggest you University School of Business (USB), Chandigarh University ranked among the Best Management Colleges in Punjab has earned recognition for its unique style of teaching & experiential learning. The attribute that makes learning business management exclusive at USB is its specialised approach paired with a research focus, innovation culture and entrepreneurship zeal backed by world-class facilities.

https://www.shiksha.com/distance-mba-mba-distance-education-chp
You will find all the true and authentic information here.

Iims do not offer Distance MBA courses. So, you, can opt for Diploma and certification courses for working professionals offered in Distance Learning mode.

You can get admission to Delhi University and you will get the best professors.

No, it's not necessary that entrance is compulsory. It varies from course to course and college to college.

IIBM is supposed to be good in comparison to NIBM.

Though it depends from college to college but it will cost you around 2 to 4 lacs.