Hello aspirant,

You haven't mentioned the rank in which competitive exam you wish to know of or even the branch you wish to pursue that is medical or engineering. Since most of the important details are lacking, I wouldn't be able to give a concrete answer. Try mentioning the exact details and then revert back in the comments.

Also the rank vs cutoffs vary every year for the different institutions. To know about the list of colleges, here are a few college predictor tools that might be of help:
https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer

https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer