My mains percentile is 88 and my category rank is 40k....will I get any IIIT...!?!?
IIIT is among the premium engineering institutions of our country and takes admission on the basis of JEE-Main rank.
With your above mentioned percentile and category rank, it'll be difficult for you to fetch a seat in any IIIT, but I'll suggest you to wait till the last rounds of counselling as it may fetch you a seat in a non-core branch in lower IIIT.
For more details about the cutoff of various IIITs, click on the link below:-
https://engineering.careers360.com/articles/jee-main-cutoff-for-top-iiits
Hope this helps.
Good Luck!!