CAT is not your final destination, but a good way to get intoa good Business School, right? CAT has an eligibility criterion of 50% in UG, so you'll not be eligible for CAT. However, there are other MBA entrance examinations, like NMAT, CMAT, MAT, etc. Many good business schools consider such exams. Private Business schools also have their own entrance exams, like IBSAT (for IBS), WAT (for Woxsen School of Business), etc. So dont get disheartened.

You may try Woxsen School of Business Hyderabad. It is a good Business School, based out of Hyderabad. They have good faculty (80% from IIM ABC), excellent grooming program, corporate exposure, international program and good placement (100% placement with high average package, INR 8LPA). Highest package goes upto INR 23LPA or even more. One of their faculty is Prof Soumyadip Chakraborty, you may connect with him and find out more. Overall, donot get disheartened, you have many good options. Try them out. All the best!