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JEE Main & Advanced Sample Paper JEE Main Sample Paper-47

  • question_answer
    Let \[f(x)={{x}^{2}}-5x+6,\]\[g(x)=f(|x|),\]\[h(x)=|g(x)|\] and \[\phi (x)=h(x)-(x)\] are four functions where \[(x)\] is the least integral function of \[x\ge x\]. Then, the number of solutions of the equation, \[g(x)=0\] is

    A)  0                                

    B)  2                 

    C)  4                                

    D)  6

    Correct Answer: C

    Solution :

      Given \[g(x)=0\] \[\Rightarrow \]            \[f(|x|)=0\] \[\Rightarrow \]            \[{{x}^{2}}-5|x|+6=0\] \[\Rightarrow \]            \[\left\{ \begin{matrix}    {{x}^{2}}-5x+6=0,\,\,x\ge 0  \\    {{x}^{2}}+5x+6=0,\,\,x<0  \\ \end{matrix} \right.\] \[\Rightarrow \]            \[\left\{ \begin{matrix}    x=2,\,3,\,\,x\ge 0  \\    x=-3,\,-2,\,\,\,x<0  \\ \end{matrix} \right.\] \[\therefore \]    Number of solutions = 4


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