Hey Shiva, if I am not mistaken you are referring here to your ST category rank to be 40K, which is really miserable as it places you at the very end in the rank list and your score must be in negatives to get such a low rank. At this rank your percentile is predicted to be around 0th percentile according to 2021 JEE Mains trend. If this is the case, then I'm really sorry Shiva, but engineering is not for you, and you completely need to change your viewpoint of your academics life.

However I would be very happy if my assumption is wrong and you actually have the CRL rank as 40K with ST category as it fetches you a percentile of around 95.5 - 95.6 approx, which is a decent performance. In this combination, you might not get core branch in NITs but as you desired for any branch, that is surely possible in the CSAB Special counselling rounds. You can use the college predictor to find the best colleges for yourself: https://engineering.careers360.com/jee-main-college-predictor?utm_source=qna&utm_medium=jee_cp

Also I would like to add a few courses at NITs available at this rank:

• MNIT Jaipur, Mechanical Engg.
• MANIT Bhopal, Chemical Engg.
• MNNIT Allahabad, Chemical Engg.
• MANIT Bhopal, Mechanical Engg.

And a lot other options. Hope that helps, do specify your query in the comments, thanks!