CAT

Hi Akshat,
Yes, you are eligible to appear for CAT exam. You need to register yourself on the official website given below:
https://www.aicte-cmat.in/College/Index_New.aspx
All the best.

30.42 [percentile won't fetch you any college.

Keep practicing the concepts regularly. Do join a good test series and evaluate your performance regularly. Work on the weaker sections and try to solve questions in minimum time. Time plays a big role in CAT. Just work hard and be determined to prepare continuously.

CAT syllabus is more of 9th and 10th mathematics and english vocabulary ( questions are like jumbled sentences, punctuation, missing words). B.Tech is more of technical subjects. Data Interpretation and Logical Reasoning are also there in CAT syllabus.

You just need to get a mere 80-82 percentile to clear the cutoff and then you have to excel best in the IRMA Aptitude Test and then convert it with your expertise. Upvote and follow if found useful.

Your chances of getting a call from IIMs are not that good, but if you score good marks like more than 99 percentile then you can get a call but in PI, you need to give a valid reason regarding your gap of 2 years.

It is going to be very difficult for you to get an admission in IIM Bangalore, without some good Work Ex and CAT marks, as IIMB gives graduation marks very high weightage in comparison to other colleges. And, after getting in you will actually need work extra hard to justify the lower marks in graduation that you have (but, with hardwork that is possible.)
Anyway, you can also look at IIM C and L which don't give as much emphasis to past acads.
Good luck.

Since you have not mentioned your university, it is quite difficult to say. But, in general, it sure does seem possible. A lot depends on the marks of people around you (as IIM Bangalore grades your marks relative to others and then gives your application some points). Anyway, it does seem possible, just score as high as possible in your CAT.