Mahesh, NITs & IITs are primarily fine engineering institutions. But over the years the Schools of managment at IITs have picked up very well. And entry in some of these like DOMS,IIT Delhi or DOMS IIT madras is quite difficult.  There ir CAT cut offs is beyond 90 percentile. 

On the other hand the Departments of Management in NITs did not quite take off. Though some like the department fo management studies at NIT Trichy were quite popular in early 2000s but have lost out the newer IIMS recently. 

We have very little information about DOMS at NIT calicut. So can not comment on the same. But on the whole. I think NIT calicut accepts both CAT and CMAT.