Hello Buddy! Hope you're doing good.

Yes, ones can do their B.Tech. and simultaneously prepare for UPSE exam. Well it totally depends on the students ability, their management capacity, and their hard work with a lot of consistency. Just make sure, if you decided to do both of them simultaneously then first focus on your grades (not fail at any cost) then if you are able to manage both then go ahead. In engineering, there's enough time you will get for doing your other entrance exam preparation. Hope this will help you.

ALL THE BEST! WORK HARD !!