Colleges in Bhubaneswar

You can see:
https://www.shiksha.com/college/ximb-Bhubaneswar-xavier-institute-of-management-xavier-university-54299/admission#admission
Also:
https://www.shiksha.com/mba/cat-exam?rf=searchWidget&landing=ep.

Please visit the link to know the details: https://www.shiksha.com/university/utkal-university-bhubaneswar-23072/admission#admission

Yes, Institute of Engineering and Management Studies offers distance courses, and you may do your M.Sc. from here. For more information, you may please check this link too- https://www.shiksha.com/college/institute-of-engineering-and-management-studies-bhubaneswar-36313

It is on the basis of marks obtained in the last qualifying exam i.e. 10+2.

No, but you have to fulfill minimum attendance to give exams.

For CMAT the minimum percentile required is 60 and for CAT it is 50.

Infrastructure wise, Bhubaneswar is better, as it is having a lush green 16 acres campus. The faculty of IMI-B is also better than that of Kolkata. Placement scenario is almost the same for both the colleges. Both are student driven. IMI Bhubaneswar was established before Kolkata. Overall, I would say it's just a 19:20 ratio difference between both of them. So, you can chose any one. Decision is up to you.