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Yes many universities give admission on basis of graduation marks. You should try to give institutional entrance exam if possible. There are few good MBA colleges like Jamia, LPU, AMU, Christ University which conduct their own MBA entrance exams
Few good option could be- LPU
- Chandigarh University
- IIHMR Jaipur ( MBA Healthcare management)
- Jamai
- AMU
- Christ University
- KIIT
- Bharti Vidyapeth ( BVU CET)
- UPES
- Allahabad University ( conduct it's own MBA exam)
- Chitkara University
- Alliance University
Academic fees for these colleges range from 1lakh ( Jamia) to 10 Lacs. Due to covid impact some colleges are giving exemption to test score. You can also explore on the option of distance MBA from Symbosis, Kurushetra, NMIMS, IGNOU. SCDL PGDM in HRM is a good option for higher study along with job. Later on you can pursue executive MBA from IIM, XLRI, FMS etc. MAT conducted 4 time a year is another option. You can refer b school ranking to shortlist colleges.

For appearing in IIT JAM you have to clear the cut-off marks, but some candidates can't score that cut-off and failed to take part in IIT JAM counseling. CCMN counseling is the Centralized Counselling for M.Sc. /M.Sc. (tech) in which candidate who failed to appear in IIT JAM counseling, can get admission to the National Institute of Technology (NITs) and Centrally Funded Technical Institute (CFTIs). It means no need to lose hope if you don't get IITs, you still have the opportunity to get admission in NITs and CFTIs. To get admission. And you need to apply for NIts after giving you the IIT JAM exam because filling the counseling form you have to submit your IIT JAM score on the basis that NITs will select you.