Hey there, You may get IIT and NIT and other state government College through jee mains rank if and only your cut off is clear, and your NATA score is eligible on only on private institute and some states university. You can try on sir J.J college of architecture through entrance exam and in jadavapur university you have to give their state exam wiz. WBJEE or  their university entrance exam.

To know more about colleges visit the link

https://engineering.careers360.com

All the best!!