My brother is an alumnus of CUSAT and according to him, the best branch to opt for at the institute is Naval Architecture and Shipbuilding. It is the flagship course offered by the university.To get admission into this branch you will need a rank less than 500 in the CUSAT CAT or a relaxed rank depending on the category of reservation you have.

Here is the required cutoff for Naval Architecture and Shipbuilding according to 2020 trends.

Hope this clears your doubts.