Distance/Correspondence MBA

Fees structure is 51k for 2 years and it offers specialisation in finance ,marketing , human and resource ,tourism, cooperate law , information and technology.

Best Universities Offering Distance Education MBA in Human Resource Management (HRM):
ICFAI University
Annamalai University
IGNOU
Suresh Gyan Vihar University
Amity University
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https://www.shiksha.com/university/nmims-university-Mumbai-52743
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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
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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.