CAT

CAT wants minimum 50% in any UG degree.
UPSC wants minimum 55% any UG degree.
MPSC wants any UG degree.
In all the three, if last semester is left then also you can apply.

You do not have to have maths as a subject in you grad course to take CAT exam. But 10th standard level maths is there in the exam so you'll have to prepare for it in any case. You can definitely take CAT exam.

Practice is the only key to success in CAT. Questions are very easy and given sufficient time, everyone will be able to solve all the questions. The trick is to solve the questions when time is a constraints. Hence speed and accuracy matters a lot.I would suggest you improve on these two factors and practice is the only way to do that.

You must give CAT or GMAT to get into IIM-Trichy.

No, it's not necessary to have mathematics.

Most of the MBA entrance exams such as CAT use concept of percentile, not percentage, for calling candidates for interview. If you score above 95 percentile, you will definitely get interview calls from few top 30 B-schools.

You need to secure 50% in your graduation to appear for CAT.

Arun sharma books are best for all 3 segments I.e quant, verbal, logical. You can also refer to study material of some coaching institute