UPCAT

Sorry to say but your rank is too high so you won't get any government college through UPTU. Try in some good private engineering colleges.

Refer the following:
https://www.shiksha.com/b-tech/resources/upsee-college-predictor

Since from this year (2017) onwards, HBTI (HBTU to be more specific) has withdrawn from UPSEE Counselling procedure and will take students through JEE Mains counselling so IET will now be the first preference of UPSEE candidates.
In 2016 surely you would have grabbed a seat in IET but not this year because now the cutoff rank will be much higher and close to the cut off rank of HBTI last year (2016).
It's quite difficult to get a core branch but you'll definitely grab a seat if you go for non-core branches in IET.
You can try for KNIT, Sultanpur or JSS, Noida if you priority is branch rather than college.

You might have a chance if you have any reservation criteria else give it a try. You have very great chances to get into this institute, with this rank. Attend the counselling and choose your options appropriately. Try Shiksha college predictor for better analysis.

GN means general caste category and BC means backward caste category.

You might have a chance if you have any reservation criteria else give it a try. You have very great chance to get into this institute with this rank. Attend the counselling and choose your options appropriately. Try Shiksha college predictor for better analysis.

Considering you're from general category, for mechanical you have slim chance though you may get some non-core branches.

You can only get private colleges with this rank, checkout Shiksha.com UPSEE college predictor to get a better idea.

Your chances would be high but you must check the official website of the college.