In order to get admission in government colleges of WB for B.tech programme you should appear for WBJEE exam

You can check the eligibility criteria of WBJEE from the given below link

WBEE Eligibility Criteria

Good Luck!!

To get admission in any good engineering college you will have to appear for engineering exams like JEE MAINS, JEE Advanced, BITSAT, VIT, SRM etc.. Based on your percentage in 12th, you are eligible for btech exams.

To get admission in West Bengal engineering colleges you can also appear for state level exam that is WBJEE.

To apply for WBJEE exam, the minimum age requirement is 17 years and there is no maximum age criteria. You should have qualified 10+2 with Physics and Mathematics along with any one of Chemistry/ Biology/ Biotechnology/ Computer Science/ Computer Application as compulsory subjects. Also you should have a domicile of West bengal. 

After successful attempt of the exam and on basiis of your rank you will be alloted colleges accordingly in West bengal.

Good Luck.