https://www.google.com/amp/s/engineering.careers360.com/articles/cusat-cat/amp

As per the admission guidelines, there is no mention of admission to CUSAT via JEE Mains score. For admission to CUSAT ,you need to sit for CUSAT CAT or CBT. The dates for the submission of application is not over yet, you can still apply.

Hope this helps.

Hello,

Well! Obviously you can't, you have to appear in CUSAT exam , there is no option to do counselling for CUSAT colleges through jee marks or ranks , you have to apply with CUSAT rank .so ,it's complusery to appear in CUSAT exam for taking admission in CUSAT colleges !

All the best !!