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JEE Main & Advanced Sample Paper JEE Main Sample Paper-20

  • question_answer
    If \[x\ne 2,\,\,y\ne 2,\,\,z\ne 2\] and\[\left| \begin{matrix}    2 & y & z  \\    x & 2 & z  \\    x & y & 2  \\ \end{matrix} \right|=0\], then the value of\[\frac{2}{2-x}+\frac{y}{2-y}+\frac{z}{2-z}=\]

    A) \[1\]                                     

    B) \[0\]

    C) \[3\]                                     

    D) \[4\]

    Correct Answer: B

    Solution :

    \[0=\left| \begin{matrix}    2 & y & z  \\    x & 2 & z  \\    x & y & 2  \\ \end{matrix} \right|=\left| \begin{matrix}    2 & y & z  \\    x-2 & 2-y & 0  \\    x-2 & 0 & 2-z  \\ \end{matrix} \right|\] \[=(x-2)(2-y)(2-z)\left| \begin{matrix}    \frac{2}{x-2} & \frac{y}{2-y} & \frac{z}{2-z}  \\    1 & 1 & 0  \\    1 & 0 & 1  \\ \end{matrix} \right|\] \[\Rightarrow \] \[0=\frac{2}{x-2}-\frac{y}{2-y}-\frac{z}{2-z}\Rightarrow \frac{2}{2-x}+\frac{y}{2-y}+\frac{z}{2-z}=0\]


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