I can only answer regarding engineering. I think you have a decent chance at Rutgers but I would also apply to NJIT and Rowan.
You can find the admissions profile for Rutgers at 2021 Admissions Profile.pdf (rutgers.edu)
And why I think that applying to NJIT and Rowan is always a good idea at Side discussion thread for top New Jersey engineering students looking for advice getting merit aid - Financial Aid & Scholarships - College Confidential Forums
Why Purdue? What does “no budget” mean?