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Question

If a=π3e,b=3πe and c=e3π, then


A

a<b<c

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B

b<a<c

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C

c<a<b

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D

a<c<b

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Solution

The correct option is A

a<b<c


Let f(x)=x1/x,x>0logf(x)=1xlogxf(x)f(x)=1x21x2 logx=1logxx2f(x)=1x2f(x)(1logx)<0 if x>e
Thus, f(x) decreases on (e,).
As e<3< π, we get
f(π)<f(3)<f(e)(π)1/π<31/3<e1/eπ3e<3πe<e3π or a<b<c.


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