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JEE Main & Advanced AIEEE Solved Paper-2009

  • question_answer
    Let a, b, c be such that\[b(a+c)\ne 0\]. If \[\left| \begin{matrix}    a & a+1 & a-1  \\    -b & b+1 & b-1  \\    c & c-1 & c+1  \\ \end{matrix} \right|+\left| \begin{matrix}    a+1 & b+1 & c-1  \\    a-1 & b-1 & c+1  \\    {{(-1)}^{n+2}}a & {{(-1)}^{n+1}}b & {{(-1)}^{n}}c  \\ \end{matrix} \right|=0,\] then the value of n is     AIEEE  Solved  Paper-2009

    A) zero      

    B) any even integer             

    C) any odd integer

    D) any integer

    Correct Answer: C

    Solution :

    \[\left| \begin{matrix}    a & -b & c  \\    a+1 & b+1 & c-1  \\    a+1 & b-1 & c+1  \\ \end{matrix} \right|\] \[+\left| \begin{matrix}    {{(-1)}^{n+2}}a & {{(-1)}^{n+1}}b & {{(-1)}^{n}}c  \\    a+1 & b+1 & c-1  \\    a-1 & b-1 & c+1  \\ \end{matrix} \right|\] \[=\left| \begin{matrix}    a(1+{{(-1)}^{n}}) & (-b)(1+{{(-1)}^{n}}) & c(1+{{(-1)}^{n}})  \\    a+1 & b+1 & c-1  \\    a-1 & b-1 & c+1  \\ \end{matrix} \right|=0\]


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