yes, 12,000 JEE Advanced rank is enough to get into an IIT — but branch and campus choices are limited. total IIT seats are 17,385+ so you're well within range.
what's realistic at 12,000 AIR (general category):
important thing most people miss — your category rank matters more than AIR. if you're OBC/SC/ST, a 12,000 AIR can unlock significantly better IITs and branches. check your category rank separately. also, newer IITs like Bhilai and Goa have been steadily improving placements and research output — don't write them off just because they're newer.
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