Which college can I get for B.Tech with 1,37,656 rank in the engineering entrance exam?

Just go through this link and fill out the required details: https://www.shiksha.com/college-predictor

The chances of getting a college are zero but you can try your best upto the last round of the counselling and as in that round there might be some seat left and you might get that seat at this rank.

Hi, The best way to predict a college through JEE Mains score is using Shiksha college predictor: https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor It shows perfectly accurate results. After that, just go for the counseling of that college. Best of luck for your future.