Hi Aashi,
                Yes definitely you are eligible for CAT. The part is you have stream diversity. Because most of engineers do MBA, but as you are non-engineer, so if you score good in CAT, you have chances to get IIM A, B, C.
On the otherhand, you have also great academics, that will help you to make a strong profile. & work-ex is not mandatory. Yes, there has points on work-ex but if you score good in CAT, all will be good.
Also as you are doing masters, you will get extra benefit for it.
So, overall you have great chances to get admission in top IIM'S and other B-Schools. You can also target FMS for ROI factor.
So, prepare well for CAT & try to score 99 percentile in CAT. & have some general knowledge of MBA.

Hope you get it.

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