The value of n is
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The value of ( n ) is
(a) 0
(b) -1
( (c) 1 )
(d) none of these

JEE/Engineering Exams
Physics
Solution
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The value of n is
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( 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)=sin ^{-1}left(frac{x}{a}-1right) )
( =sin ^{-1}left(frac{x}{a}-1right)=a^{n} sin ^{-1}left(frac{x}{a}-1right) )
( Rightarrow {a^{n}=1})  ({n=0} ) Option (a)

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