IIM

Hi,
List of some good and reputed colleges for MBA apart from IIMs:
Xavier Labour Relations Institute
FMS
National Institute of Industrial Engineering
Xavier Institute of Management, Bhubaneswar
Department of Management Studies, Indian Institute of Technology Delhi
Jamnalal Bajaj Institute of Management Studies
Vinod Gupta School of Management (IIT Kharagpur)
T. A. Pai Management Institute
Shailesh J Mehta School of Management, IIT Bombay
Birla Institute of Management Technology, Greater Noida
Institute of Management, Nirma University
Goa Institute of Management
Lal Bahadur Shastri Institute of Management
National Institute of Agricultural Extension Management
DOMS, National Institute of Technology, Trichy
Loyola Institute of Business Administration
Bharthidasan Institute of Management

Hi Adrita,
IIM Bangalore as such does not have any minimum cutoff percentage in class 10th, 12th or Bachelors, which you need to clear. However, it assigns a weight of 50% (20% for 10th, 10% for 12th and 20% for bachelors score) and thus, it would be difficult to get a call from IIM Bangalore (refer to http://www.iimb.ac.in/sites/default/files/iimb-pgp-admission-process.pdf). IIM Ahmedabad on the other hand has a minimum cutoff percentage which is set at 80 percentile score. Thus, looking at your graduation score, it would be impossible to get a call from IIMA (unless you are in top 20 percentile at your college, please refer to https://web.iima.ac.in/users/admission/files/Shortlisting Criteria for PGP 2017-19 batch_110117.pdf).
However, having said that, there are many top B-schools who will consider you provided you could score a respectable score in CAT. Therefore, your aim to be to maximize your CAT score. All the best.