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## QuestionPhysicsClass 11

Given that $$\int\frac{{{\left.{d}{x}\right.}}}{{\sqrt{{{2}{a}{x}-{x}^{{2}}}}}}={a}^{{n}}{{\sin}^{{-{1}}}{\left(\frac{{{x}-{a}}}{{{a}}}\right)}}$$ where a is a constant. Using dimensional analysis. The value of n is
(A) 1
(B) -1
(C) 0
(D) none of the above.

The integral on LHS is in the from of log x, which is a number. Hence, $${a}^{{n}}$$ must be a number, for which n = 0