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Based on your CAT percentile of 35.68, you may have limited options for MBA colleges. However, there are still many colleges that you can apply to based on your academic background. Some of the colleges you can consider are:
Institute of Management Technology, Nagpur
Institute of Management Technology, Hyderabad
Amity Global Business School, Noida
Alliance School of Business, Bangalore
VIT Business School, Vellore
Jagan Institute of Management Studies, Delhi
Please note that the final selection for admission also depends on other factors like your work experience, extracurricular activities, and performance in the selection rounds of the respective colleges. Please upvote if it was helpful.

With a CAT percentile of 81 and a background in Mechanical Engineering, you may have a chance of receiving a call from MANAGE Hyderabad (National Institute of Agricultural Extension Management). However, admission to MANAGE Hyderabad depends on several factors such as the number of seats available, the number of applicants, and the cutoff percentile for the year.
MANAGE Hyderabad uses CAT scores as one of the parameters for shortlisting candidates for its Post Graduate Diploma in Management (Agri-Business Management) program. However, the final selection is based on a candidate's overall profile, which includes academic record, work experience, performance in GD-PI rounds, and other factors.
Therefore, while your CAT percentile is a good starting point, I suggest that you focus on improving your overall profile, including your academic record, work experience, and communication skills, to increase your chances of getting shortlisted and selected for the program.