Hello Aspirant,

According to the category rank you have mentioned in the question you cannot get NIT Patna or even any of the NITs as per previous year's cut-offs which you can check out from the link given below :-

https://engineering.careers360.com/articles/jee-main-cutoff-for-nit-patna

But yes I would suggest you to sit for some state counselling because in some of the state government colleges you can get admission on such ranks.

Note that the cut-offs are bound to change every year depending upon various factors.

Now as you are asking about change of branch for integrated courses so yes you can change but the condition is that you must fulfil the eligibility criteria for branch change as per the institution because there are different institutions and have different eligibility criterias.

You can use JEE-Main College Predictor to predict your chances of admission in different engineering colleges of India :-

https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

I hope this information helps you.

Good Luck!!