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

Securing a rank of 3000 in JEE Advanced is a commendable achievement, and it will open up a wide range of opportunities for you in terms of college choice. With a rank of 3000, you have a good chance of getting admission into IIT Bombay, but you may not get your desired domain.

With this rank you can get admission in these specialisations at IIT Bombay: 

• Environmental Science and Engineering
• Civil Engineering
• Metallurgical Engineering and Materials Science

You can visit the official JoSAA website to check the previous year IIT Bombay branch wise cutoff for B.Tech Admissions- https://josaa.admissions.nic.in/applicant/seatmatrix/openingclosingrankarchieve.aspx

This will give you a better understanding of your options.

I have listed below the JEE Advanced 2023 cutoffs for IIT Bombay for the OBC NCL category for your reference:

IIT Bombay BTech Cutoff 2023 for OBC NCL 

I hope the previous year's cutoff will give you an idea of the general trend followed by IIT Bombay for admissions of OBC NCL candidates through JEE Advanced.