You are giving Board Exam in  Kerala, therefore, Your state of eligibility will be Kerela and Not Tamilnadu, Therefore You will get benefits of Home state quora in the NIT Calicut and Not in the NIT Trichy

Cutoffs are Not fixed they change every Year, Becuase difficulty level of the exam varies every year and also Number of students, But there is a regular trend in the Opening closing ranks So You can see What is the minimum rank You require to get admission into NIT. It also depends on the lot of factors such as what is Your category, what Branch are You interested in So Please follow the link below to find the closing Of Your course under a specific category.

https://josaa.nic.in/josaaorcrarchieve/Result/OpeningClosingRankArchieveN.aspx?Year=2017