If JEE main marks is 150 and Bihar board marks is 60% than which of the government college can get

Now it's all dependent on Bihar Board. If you fall in the top 20 percent of the students in Bihar Board you can get NITs but if you miss it,I am sorry but you wouldny be able to get any college through JEE Mains.
But you can always wait as sometimes in The CSAB round when many seats remain vacant sometimes they rest their board criteria and thus allow students with lower board marks to get Seats

So you should wait and just pray for some luck to be beside you side.
Your JEE marks are good but I think board marks can land you in trouble.
Hope this helps.
Best of luck!!!