Hello Vijay,

Yes you can write both exams. For most of the engineering exams, now you have the option for slot booking. Unlike previous old days, now you can book the good day on which you will like to appear for the exam among a week during which exams are conducted. You may select the different dates for both exams. In case of VITEEE exam you have the option to even modify your exam date prior to the exam, so you can reschedule your exam, in case of any emergency.

Hope this Helps