Yes, there are a total of 17,385 seats in the IITs, you can get admission into IITs with a rank of 12k in JEE Advanced. However, you will probably not get admission in top 7 IITs and in the branches which are the favourites of the most people. But indeed you can get admission into IITs with 12,000 rank in JEE Advanced.
You can visit the official JoSAA website to check the previous year cutoff trends for B.Tech admissions at the IITs- https://josaa.admissions.nic.in/applicant/seatmatrix/openingclosingrankarchieve.aspx