JEE

Yes, you can get admission through the direct admission process by simply visiting their official website by filling out the admission form and the fees.

You cam check it by just visiting the below link and fill the required fields. https://www.shiksha.com/engineering/jee-main-college-predictor

You can check it on below mentioned link https://www.shiksha.com/engineering/jee-main-college-predictor

You can predict your college on the below mentioned link https://www.shiksha.com/engineering/jee-main-college-predictor

No chance of getting admission in government colleges as the rank below 50000 are considered safe to get the admission in government colleges but your rank doesn't match the criteria. 

You can get the best results for your query on this attached link https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor? utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7489993

JNGEC offers 4 courses for B.E. and the eligibility criteria is:-

45% in HSC Board 10+2, based on marks in JEE.

There is no cutoff specified for JEE Main. As it is a government college it will take a cutoff as specified by NTA for JEE Main Admission

Any way if you have qualified the entrance then you should apply for it. you will get it with your categorical rank and if you have home state quota the that will be better.

Yes ofcourse many college accept JEE Mains as there admission entrance exam. You can easily into NIT with valid score even though you can get admission outside india as well. 31 NIT and different private college give admission on Jee Mains score. You can easily get into any NIT with good score in JEE mains. 

Thank You

As far as I know, It's true that you can get a seat at 8 lakh but you can't take that risk because you are also loosing hope for 3rd tier colleges, now  better look for private colleges.