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KVPY Sample Paper KVPY Stream-SX Model Paper-10

  • question_answer
    If \[a<0,\] \[f\,(x)={{e}^{ax}}+{{e}^{-ax}}\]and  S = {x ; f(x) is monotonically decreasing}; then S equals

    A) {x : x > 0}                   

    B) {x : x < 0}

    C) {x : x > 1}                   

    D) {x : x < 1}

    Correct Answer: B

    Solution :

    \[{{f}^{1}}\,(x)=a\,({{e}^{ax}}-{{e}^{-\,ax}})<0\]
    \[\Rightarrow \]   \[{{e}^{ax}}>{{e}^{-\,ax}}\]                      \[(\because a<0)\]
    \[\Rightarrow \]   \[x<0\]


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