InterviewSolution
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InterviewSolution
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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-1B. Statement-1 True statement -1 is True,Statement -2 is True statement -2 is not a correct explanation for Statement-1C. Statement-1 True statement -1 is True,Statement -2 is FalseD. Statement-1 is False ,Statement -2 is True |
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Answer» Correct Answer - 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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