There would be no use of merely getting a degree such as MBA through distance education. For better career growth go for regular degree. Some good institutes are :IIMs

Xavier's Labour Relations Institute, Jamshedpur

Indian School of Business ,Hyderabad,

Lovely Professional University, Punjab

K.J. Somaiya Institute of Management Studies and Research Mumba

Lal Bahadur Shastri Institute of Management Delhi

Management Development Institute (MDI), Gurgaon

Narsee Monjee Institute of Management Studies, Mumbai

National Institute of Industrial Engineering , Mumbai

Faculty of Management Studies , Delhi

ICFAI Business School, Hyderabad

Jamnalal Bajaj Institute of Management Studies, Mumbai

International Management Institute New Delhi

Yes you must have minimum 50%aggregate marks in graduation and can apply to Onljne MBa program from NMIMS and IGNoU and Welingkars which are top institute 

Based on written test / Graduation scores you shall be eligible for admission..

Also you need to verify all documents as per college policies and then admission shall take place.