Hi Aspirant,

There is no such official reports about anything as such that 11th dropper can't give 12th KVPY SX. So Yes, you can certainly try out and apply for KVPY SX. Also the eligibility criteria says that the candidate should be enrolled in Class 12 in the year of giving KVPY SX exam and the minimum marks required is aggregate 75% (65% for SC/ST/PWD) in Mathematics and science subjects in class 10th exams.

For further information related to KVPY refer the link below,

https://school.careers360.com/articles/kvpy

Hope this helps.

Good luck!!!