Can a general student still get admission to any government college if he didn't even qualify the cutoff of jee mains...

Its next to impossible to secure seats in any government backed good college.
Jee mains ismust for all GFTIs.
One must qualify with 200 and above marks to secure seats in all top tier NITs and GFTIs.

The list of all 20 participating institutions under government backing shared below.

https://www.google.co.in/amp/s/engineering.careers360.com/articles/jee-main-participating-institutes%3famp

https://www.google.co.in/amp/s/engineering.careers360.com/articles/list-of-government-funded-technical-institutes-gftis%3famp

Hello,
Well it is too difficult for any student to get admission in government colleges with marks having lesser than the cutoff marks.To get admission in government colleges you should score atleast 200+ in jee mains because the competition is too high and if you can prepare well for it then only you will succeed.
Good luck.