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JEE Main & Advanced Sample Paper JEE Main Sample Paper-27

  • question_answer
    If non-zero real numbers b and c are such that min. \[f(x)>\] max. \[g(x)\], where \[g(x)=-{{x}^{2}}-2cx+{{b}^{2}}(x\in R)\] and\[g(x)=-{{x}^{2}}-2cx+{{b}^{2}}(x\in R)\] then \[\left| \frac{c}{b} \right|\] lies in W interval

    A)  \[\left[ \frac{1}{\sqrt{2}},\sqrt{2} \right]\]                       

    B)  \[\left( \sqrt{2},\infty  \right)\]

    C)  \[\left( 0,\frac{1}{2} \right)\]                  

    D)  \[\left[ \frac{1}{2},\frac{1}{\sqrt{2}} \right]\]

    Correct Answer: B

    Solution :

    We have \[2{{c}^{2}}-{{b}^{2}}>{{b}^{2}}+{{c}^{2}}\] \[\Rightarrow \,{{c}^{2}}>2{{b}^{2}}\] \[\Rightarrow \,\,\,\left| \frac{c}{b} \right|>\sqrt{2}\]


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