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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 13

  • question_answer
    Let \[f(x)\] be a continuous function on R and \[f(0)=f(2),\] then the equation \[f(x)=f(x+1)\] will have

    A)  At least one root in \[[0,\,1]\]

    B) At most one root in \[[0,\,1]\]

    C) Exactly one root in \[[0,\,1]\]

    D) No root in \[[0,\,1]\]

    Correct Answer: A

    Solution :

    [a]   Consider \[h(x)=f(x)-f(x+1)\] \[h(0)=f(0)-f(1)\] \[h(1)=f(1)-f(2)=f(1)-f(0)\] [Given \[f(0)=f(2)\]] i.e., \[h(0)\] and \[h(1)\] are of opposite signs and \[h(x)\] is continuous function. Hence, \[h(x)\] will have at least one root in \[(0,\,\,1)\] or \[[0,\,\,1]\].


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