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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2005

  • question_answer
    If\[p{{\lambda }^{4}}+q{{\lambda }^{3}}+r{{\lambda }^{2}}+s\lambda +t=\] \[\left| \begin{matrix}    {{\lambda }^{2}}+3\lambda  & \lambda -1 & \lambda +3  \\    \lambda +1 & 2-\lambda  & \lambda -3  \\    \lambda -3 & \lambda +4 & 3\lambda   \\ \end{matrix} \right|\] then\[t\]is equal to:

    A)  33         

    B)                         22

    C)  21    

    D)         \[-33\]

    E)  54

    Correct Answer: C

    Solution :

        \[\because \]     \[p{{\lambda }^{4}}+q{{\lambda }^{3}}+r{{\lambda }^{2}}+s\lambda +t=\] \[\left| \begin{matrix}    {{\lambda }^{2}}+3\lambda  & \lambda -1 & \lambda +3  \\    \lambda +1 & 2-\lambda  & \lambda -3  \\    \lambda -3 & \lambda +4 & 3\lambda   \\ \end{matrix} \right|\] \[\Rightarrow \]               \[p{{\lambda }^{4}}+q{{\lambda }^{3}}+r{{\lambda }^{2}}+s\lambda +t\]                 \[=({{\lambda }^{2}}+3\lambda )(5\lambda -4{{\lambda }^{2}}+12)\] \[-(\lambda -1)(2{{\lambda }^{2}}+9\lambda -9)+(\lambda +3)(2{{\lambda }^{2}}+10)\] On comparing both sides, we get \[t=-9+30=21\]                 


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