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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 35

  • question_answer
    If \[y=f(x)\] is discontinuous at exactly three points \[{{\alpha }_{1}},{{\alpha }_{2}}\] and \[{{\alpha }_{3}}\] where \[{{\alpha }_{i}}<0\,\forall \,i=1,2,3,\]then function \[y=f\left( -|3x-1| \right)\]is discontinuous at \[x={{\beta }_{1}},{{\beta }_{2}},......{{\beta }_{n}}\]The value of \[\sum\limits_{i=1}^{n}{{{\beta }_{i}}}\] is

    A) 2                 

    B)        3                        

    C) 4                        

    D)        8

    Correct Answer: A

    Solution :

        [a] $-|3x-1|={{\alpha }_{1}}$ $\Rightarrow \,\,\,\,3x-1=\pm {{\alpha }_{1}}$ $\Rightarrow \,\,\,\,x=\frac{1\pm {{\alpha }_{1}}}{3}$ Similarly, $x=\frac{1\pm {{\alpha }_{2}}}{3}$ and $x=\frac{1\pm {{\alpha }_{3}}}{3}$. $x={{\beta }_{1}},{{\beta }_{2}},.....{{\beta }_{6}}$. $\sum\limits_{i=1}^{n}{{{\beta }_{i}}=\left( \frac{1-{{\alpha }_{1}}}{3} \right)+\left( \frac{1+{{\alpha }_{1}}}{3} \right)+\left( \frac{1-{{\alpha }_{2}}}{3} \right)}$ $+\left( \frac{1+{{\alpha }_{2}}}{3} \right)+\left( \frac{1-{{\alpha }_{3}}}{3} \right)+\left( \frac{1+{{\alpha }_{3}}}{3} \right)=2$  


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