Is there any chance for a student outside Kerala to get in CUSAT?

CUSAT has a state quota that offers less or no fees scheme. No student from Kerala is offered normal or payment seats which have fees similar to the NITs. However, being a non-Keralite, you have to score a better rank than most of the Keralites. 

• Entrance to CUSAT is through an All-India Entrance exam. If you score well in the CAT, you will easily get it. 
• Getting a good rank in CUSAT – CAT is not as difficult as JEE Main but depends mainly on speed. 
• If you are a non-Keralite, a rank below 1600 would be good for you to get admission. But, a rank of 2500, may spoil your chances.

CUSATs, NRI quota has a higher admission and semester fee. You will have to appear for the CUSAT-CAT anyway. The ranks might go very low for the NRI quota. Management and sports quota are also viable options if you meet the eligibility norms. 

You need to be clear with the course you opt for. If M.Tech is your choice, you should go for GATE and then apply for admission, or else a departmental admission test. In case, counseling has been completed and seats are still vacant, the institution calls for spot admission.