Shailesh J. Mehta School of Management, IIT Bombay

https://www.shiksha.com/engineering/articles/iit-fee-structure-for-btech-blogId-6275
You will find all the true and authentic information about your college here.you have a very well chance of getting into the above colleges mentioned by you just look at the citoff.

To get admitted into any IIMss or any Top MBA colleges in India, the minimum CAT 2022 cutoff is expected to be 90 percentile. Those who secured the 99+ percentile can apply to top Iims like IIM Bangalore, IIM Ahmedabad, IIM Lucknow, IIM Calcutta, and IIM Kozhikode. Hope it helps.

No you cannot get into IIT Bombay with cat percentile of 88.

Your score was good but for the admission, you need 70% in CAT and the percentile reaches to 50, so you try to get 50% in CAT.

Yes you can apply MBA if you want to particular college go for it.

Hi Sujata, You have scored 68% in both 10th and 12th and 9 CGPA in graduation. So to kno if you can get admission in SJMSOM if you score well in CAT and you belong to NCOBC CAT then you can visit the following Shiksha link to predict the college in which you are eligible. This is Shiksha College Predictor 2022. You can predict Colleges based on exams you have taken
https://www.shiksha.com/college-predictor
Hope this helps!
Best Wishes!

Yes, you can get into any college.