MAT

If you are working, or is in the final year of graduation and is ready to give CAT next year, then surely that's the best option. You can attempt other entrances like XAT CMAT NMAT etc. And try to GET into a good college. But, do make sure you do something productive or take some new courses to add to your CV while dropping the year, because during interviews you might have to justify the year gap. Otherwise, if you don't have any high expectations on the placement side then you can right away take admission in colleges like NDIM, Jaipuria Institute, SCMS Cochin, Alliance Bangalore, ITM Navi Mumbai etc.

It's hard to manage both, but if you can, then you can go for that.

Top MBA Colleges in India Accepting MAT are mentioned at the link provided below:
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-india-accepting-mat/2-2-0-0-306
There are over 155 MBA colleges accepting ICET in India Offering 180 Courses. Please refer to the link provided below for a detailed list of these colleges:
https://www.shiksha.com/mba/colleges/mba-colleges-accepting-icet-india

Better than just selecting only one college, I would like to suggest you appear for CAT, MAT and CMAT. This will open the doors of many other good institutes for you.

The AIMA or All India Management Association conducts MAT 4 times every year and there is no limit to individual attempts, so you can appear for MAT four times in a year, However, most of the top B-Schools consider only the Dec or Feb edition of MAT so it is advisable to appear for the same
All the best.

Yes, it is valid but the thing is that in which college, you want to take admission? They will see that your marks is above eligibility criteria or not.