Hello Student, 

The general category rank for ECE home state in NIT Calicut is around 8k-13k.

But as you have mentioned 6600 is your EWS rank,  your general rank would be higher than required. 

As EWS is going to be applied for the first time, so no one is pretty sure about it,  still getting ECE in Calicut with your score is not possible. 

Hope this will help. 

Feel free to ask any doubts.