Hello Aspirant,
You don't have to worry as to clear the UPSC exam you just have to have a good grasp in every subject not just in physics chemistry and maths. And my suggestion for you is to take bachelor degree in Arts or in any stream as to crack this exam the syllabus has no similarity with the BTech and to crack it you have to study its own syllabus so focus on the UPSC syllabus and can go for bachelor degree where you can find time and can study for UPSC simultaneously.
Good luck
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