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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2008

  • question_answer
    If\[f(\alpha )=\left| \begin{matrix}    1 & \alpha  & {{\alpha }^{2}}  \\    \alpha  & {{\alpha }^{2}} & 1  \\    {{\alpha }^{2}} & 1 & \alpha   \\ \end{matrix} \right|,\]then\[f(\sqrt[3]{3})\]is equal to

    A)  1   

    B)                                         \[-4\]

    C)  4                            

    D)         2

    E)  \[-2\]

    Correct Answer: B

    Solution :

    Given, \[f(\alpha )=\left| \begin{matrix}    1 & \alpha  & {{\alpha }^{2}}  \\    \alpha  & {{\alpha }^{2}} & 1  \\    {{\alpha }^{2}} & 1 & \alpha   \\ \end{matrix} \right|\] \[=1({{\alpha }^{3}}-1)-\alpha ({{\alpha }^{2}}-{{\alpha }^{2}})+{{\alpha }^{2}}(\alpha -{{\alpha }^{4}})\] \[={{\alpha }^{3}}-1-0+{{\alpha }^{3}}-{{\alpha }^{6}}\] \[\Rightarrow \]\[f(\sqrt[3]{3})=3-1-0+3-{{3}^{2}}=6-10=-4\]


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