If the curves y=lnxx and y=λx2 (where λ constant) touch each other, then 3eλ is
A
e
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B
e2
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C
1
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D
9
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Solution
The correct option is C 1 y′=1−lnxx2andy′=2λx ⇒1−lnx=2λx3lnx=λx3} On solving these two equations simultaneously we get, lnx=13⇒x=e13 After equating y values of both curves for the calculated x we get, 13=λe⇒λ=13e