CAT

Yes you are eligible. There is no age restriction for PG / Masters Level courses in India.

Hi
You may ignore the IIMs in the list and look for other top colleges for mba and their eligibility here.
https://www.shiksha.com/mba/ranking/top-mba-colleges-india/2-2-0-0-0

Hi Chintan,
For a general category candidate with your profile, there is a small chance if getting an IIM call. In fact you may be Ineligible for a few of them. You can find your chances here -
https://www.shiksha.com/mba/resources/iim-call-predictor

No MAT is not eligible in Sathyabama university. But you can join directly over here. Admission is till the end of July.

Yes in entrance exams there is maths

You can prepare individually if your concepts are clear, if not I suggest you to join TIME ( TRIUMPHANT INSTITUTION OF MANAGEMENT EDUCATION ). It is the best Management Entrance preparation institute in India. Best of luck.

in india, pgdm is same as mba, evn u can do phd after pgdm,after aicte pgdm,u also do phd bt not ugc aspect. don't focus degree.go high rank b school.bt if u plan u will do ugc phd or outside of india. then mba degree need.

Hi,
Yes you can prepare for CAT and pursue graduation degree simultaneously. You can join weekend coaching in any institute near your place of residence for CAT preparation.

Dear Chinky,
Yes, you can apply with your CAT, you don't need to have a CET score. you can register online and upload required documents but after that, you need to go for verification of documents at nearest facilitation centre.list of centre's you can download from the website.
Good Luck!