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JEE Advanced Model Paper 13 with solutions for online practice

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Paragraph for Question Nos. 57 to 58

Let f(x) =
1
a√2π
 e−
1
2
(
x−a
b
)2 ; - ∞ < x < ∞ . Where a and b are real constants ( - ∞ < a < ∞ , b > 0) and
∞
∫
0
 xα−1ex dx = I (α) with I (
1
2
) = √π Now answer thefollowing
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