To find out which private colleges *might* be accessible with that rank, I recommend:
1. Checking the UPTU official website: The official website will likely have previous year's cutoff ranks for various private colleges. This gives the best indication of your chances.
2. Contacting private colleges directly: Call or email the admission offices of private engineering colleges in Uttar Pradesh that interest you. Ask them directly about the cutoff rank for your chosen branch in previous years.
3. Using college search websites: Websites that specialize in college admissions in India might have data on cutoff ranks, but this data may not always be perfectly up-to-date.
Remember that your chances depend heavily on the specific branch of engineering you're applying for. Some branches are less competitive than others. Also, keep in mind that the cutoff ranks can change from year to year. Don't get your hopes up too high, and be prepared to explore other options such as less popular branches or different colleges outside UPTU.