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BCECE Engineering BCECE Engineering Solved Paper-2014

  • question_answer
    If \[\left| \begin{matrix}    {{x}^{2}}+x & 3x-1 & -x+3  \\    2x+1 & 2+{{x}^{2}} & {{x}^{3}}-3  \\    x-3 & {{x}^{2}}+4 & 3x  \\ \end{matrix} \right|\] \[={{a}_{0}}+{{a}_{1}}x\] \[+{{a}_{2}}{{x}^{2}}+.....+{{a}_{7}}{{x}^{7}},\]then the value of \[{{a}_{0}}\] is

    A) 25

    B) 24

    C) 23

    D) None of the above

    Correct Answer: D

    Solution :

    Given, \[\left| \begin{matrix}    {{x}^{2}}+x & 3x-1 & -x+3  \\    2x+1 & 2+{{x}^{2}} & {{x}^{3}}-3  \\    x-3 & {{x}^{2}}+4 & 3x  \\ \end{matrix} \right|\] \[={{a}_{0}}+{{a}_{1}}x+......+{{a}_{7}}{{x}^{7}}\] On putting \[x=0,\]we get \[\left| \begin{matrix}    0 & -1 & 3  \\    1 & 2 & -3  \\    -3 & 4 & 0  \\ \end{matrix} \right|={{a}_{0}}\] \[\Rightarrow \]               \[0+1(0-9)+3(4+6)={{a}_{0}}\] \[\Rightarrow \]               \[30-9={{a}_{0}}\] \[\Rightarrow \]               \[{{a}_{0}}=21\]               


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