Because of their calculation
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None is part of the other, but the two are closely related. Lots of practical applications of math appear, precisely, in physics.
Of all the sciences, physics is very demanding for maths. So if you are really strong at maths, physics might just be for you
Giving the IIT exam is a suitable option as it has both engineering and science.
Lots of physical processes are described by mathematics. Just look into any high-school or university physics book; you will find formulae in every chapter.
they are the same