Hi Anamitra,

Predicting cutoffs and percentiles is very difficult as it is very relative. However, as much as I have studied and from a few references, your speculated percentile can be between 85-88. But as I said, it’s just a speculation so please kindly consider it like that. I will be giving you the link for the website of expected cutoffs for you to judge better, at the end of this answer. 

As for the Universities that can you apply to, if you do get a percentile in the above mentioned range then you can apply to colleges like - GIM (Goa), TAPMI (Manipal), Great Lakes (Chennai, Gurgaon), IRMA (Anand, Gujarat), MICA (Ahmedabad), K J Somaiya (Mumbai), LIBA (Chennai) and IFMR (Chennai).

Link -

www.mbauniverse.com/article/xat-score-vs-percentile

I hope this is useful to you. Please feel free to contact me for any further queries.