☆ J V2ax - x 2 The value of n is (a...
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☆ J V2ax - x 2 The value of n is (a) o (b)-1 (c) 1 (d) none of these. You may use dimensional analysis to solve the problem.

JEE/Engineering Exams
Physics
Solution
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( begin{aligned} int frac{d x}{sqrt{2 a x-x^{2}}} &=int frac{d x}{sqrt{a^{2}-left(x^{2}-2 a x+a^{2}right)}} &=int frac{d x}{sqrt{a^{2}-(x-a)^{2}}} &=sin ^{-1}left(frac{x-a}{a}right) end{aligned} ) ( Rightarrow quad sin ^{-1}left(frac{x}{a}-1right)=a^{n} sin ^{-1}left(frac{x}{a}-1right) ) ( Rightarrow frac{a^{n}=1}{mid n=0} mid ) ofinon
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