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JEE Main & Advanced JEE Main Paper (Held On 11 April 2015)

  • question_answer
    Let \[f:R\to R\]be a function such that\[f(2-x)=f\,(2+x)\] and\[f(4-x)=f\,(4+x),\]for all \[x\in R\]and \[\int\limits_{0}^{2}{f(x)}dx=5.\]Then the value of \[\int\limits_{10}^{50}{f(x)}\,dx\]is:

    A)  80

    B)  100

    C)  125

    D)  200

    Correct Answer: B

    Solution :

      \[f\left( 2-x \right)=f\left( 2+x \right)\Rightarrow \]function is symmetrical about x = 2 \[\And f\left( 4-x \right)=f\left( 4+x \right)\Rightarrow \]function is symmetrical about x - 4 \[\Rightarrow \]\[f(x)\]is periodic with period .2 \[\Rightarrow \]\[\int\limits_{10}^{50}{f(x)}dx=\int\limits_{2(5)}^{2(25)}{f(x)}dx=(25-5)\] \[\int\limits_{0}^{2}{f(x)}dx=20\times 5=100\]


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