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JEE Main & Advanced Sample Paper JEE Main Sample Paper-15

  • question_answer
    The least natural number 'k' for which  \[x+k{{x}^{-2}}>2\times \forall x\in (0,\infty )\] is

    A)  1                                            

    B)  2

    C)  3                                            

    D)  4

    Correct Answer: B

    Solution :

    Let\[f(x)=x+k{{x}^{-2}}\] \[f'(x)=1-2k{{x}^{-3}}=0\]\[\Rightarrow \]\[x={{(2k)}^{\frac{-1}{3}}}\] \[f''(x)=6k{{x}^{4}}>0\forall x\in (0,\infty )\] \[{{(2k)}^{\frac{1}{3}}}+k{{(2k)}^{\frac{-2}{3}}}>2\]\[k>\frac{32}{27}\] \[\therefore \]least natural number k = 2 Ans.


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