With a PCM UR rank of 3475 in BCECE, your chances of getting admission to a government engineering college might be limited, but it’s not impossible. Here’s what you can do:

1. Check Previous Cutoffs : Look at the cutoff ranks from previous years for various government and private engineering colleges. This will help you understand where your rank might fit.

2. Participate in Counseling : Engage in the counseling process and keep an eye on the available options. You might find opportunities in less popular branches or colleges.

3. Consider Private Colleges : If government colleges don’t work out, you might explore private engineering colleges where your rank might be competitive.

4. Stay Updated : Monitor the counseling rounds and seat allocation carefully. Sometimes, additional rounds or special quotas might offer more opportunities.

Ultimately, while government college options might be challenging, there are still several possibilities available based on your rank.