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Statement-1 e^(pi) gt pi^( e) Statemen...

Statement-1 `e^(pi) gt pi^( e)`
Statement -2 The function `x^(1//x)( x gt 0)` is strictly decreasing in `[e ,oo)`

A

Statement-1 True statement -1 is True,Statement -2 is True statement -2 is a correct explanation for Statement-1

B

Statement-1 True statement -1 is True,Statement -2 is True statement -2 is not a correct explanation for Statement-1

C

Statement-1 True statement -1 is True,Statement -2 is False

D

Statement-1 is False ,Statement -2 is True

Text Solution

Verified by Experts

The correct Answer is:
A
Let `f(x)=x^(1//x)` Then ,
`f(x)=x^(1//x)(1/x^2 - (log x)/(x^2))=x^(1//x)((1-log x )/(x^2))`f
`rArr f(x) lt 0` for all `x in (e,oo)`
`rArr f(x) ` is strictly decreasing in `[e,oo)`
`rArr (e ) gt f(pi)`
`rArr e^(1//e) gt pi^(1//pi) rArr e^(pi) gt pi^(e)`
Hence both the statements are ture and statement -2 is a correct explanation for statement -1
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