IIM Ahmedabad - Indian Institute of Management

go for MBA as it will be a better option

Check this -
https://www.shiksha.com/getListingDetail/307/institute/college-Indian-Institute-Of-Management-Ahmedabad-Iim-A-Ahmedabad-India
https://www.shiksha.com/mba/ranking/top-mba-colleges-india/2-2-0-0-0

Depends from where do you do your MBA. If you are doing it from top 30 institutes in India then definitely you will get a good career start

MBA after getting an engineering degree will be a good option to go for. Your technical knowledge and professional attitude will help you a lot to think deeply about a problem and solve it quickly and correctly. Your technical degree will provide a strong hard foundation platform for your growth on which you will construct the building of managerial skills.

Your 10th and 12th% are on the lower side, you need to score higher percent in graduation and 98 percentile in CAT. Check this link-https://www.shiksha.com/understand-the-short-listing-criteria-of-all-13-iims-article-5379-1

1) SP Jain
2) IIT
3) JBIMS
4) NMIMS

Yes you can write M.B.A exam. To get into MBA course, write CAT/XAT.MAT/CMAT exam.
Eligibility is at least 50% in graduation. You fulfills criteria for IIM-A.
Check this link-
https://www.shiksha.com/mba/course/post-graduate-program-management-indian-institute-management-iim-a/1653

Check out this link for previous year's cutoff according to colleges -
https://www.shiksha.com/minimum-cat-2015-percentile-required-for-admissions-at-iims-article-11265-1
At 90 percentile you can apply for BIM-Trichy, GIM-Goa , IFMR-Chennai and few others, but these are some good colleges. IFMR is known for Finance among corporate and it is at par with IIMs with 100% placement record. GIM-Goa is having good past track record and BIM-trichy is upcoming with disciplined study culture and decent placement record.

you have to score at least 95 percentile if you want to get selected in iim

IF you get 99%til in CAT then there will be a chance to get a call from IIm's.