Hi,
Well, It's obvious you can't .
But if you are not a citizen of India then you may get admission under Foreigner Quota.
For getting admission in CUSAT, it's compulsory for everyone to give the CAT because the roll number generated at the time of registration and the rank which you will score will be the primary identity for you.
The CUSAT CAT is the normal channel for admission to most programmes in CUSAT. But in the case of the new Integrated MSc programmes in Mathematics, Physics, Chemistry and Statistics, preference will be given to students possessing KVPY (Kishore Vaigyanik Protsahan Yojana) scholarship. They do not have to appear for CAT, but they have to apply for CAT through online and should pay the application fee.
Hope this helps.
Good luck.
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