Dear Ayush
Because of large number of private engineering colleges,  the number of government colleges seemed to be less in number but the education provided in government will be good.  And you need to take JEE mains, advanced in order to get into nit's,  IITS and you can also give your respective state entrance tests so that by getting good marks, you'll get into good government college.  This needs lot of dedication too.
All the best.

There are not many government colleges in india as compared to private colleges.To get admission in the government colleges you need to give jee mains and advanced,state level engineering entrance exams,wbjee.You need to clear these exams with very high marks to get government engineering colleges like jadavpur university,IITs,NITs.