Eligibility criteria shared below for CAT :
Since the eligibility criteria for CAT only requires a bachelors or equivalent degree with at least 50% marks, you are definitely eligible to sit for the exam.

Https://bschool.careers360.com/articles/cat-eligibility-criteria

Here's the list of Top MBA Colleges In India :

https://bschool.careers360.com/colleges/ranking/201

Do follow TIME AND CL Ratings of Top MBA COLLEGES

Entrance exams suggested are CAT/SNAP/NMAT/IBSAT/IIFT/XAT

Hope it clears your doubts.
Feel free to ask any queries

All the best for your future endeavours !!