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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2007

  • question_answer
    The coefficient of\[x\]in \[f(x)=\left| \begin{matrix}    x & 1+\sin x & \cos x  \\    1 & \log (1+x) & 2  \\    {{x}^{2}} & 1+{{x}^{2}} & 0  \\ \end{matrix} \right|,-1<x\le 1,\]is

    A)  1                                            

    B)  \[-2\]

    C)  \[-1\]                   

    D)         0

    E)  2

    Correct Answer: B

    Solution :

    \[f(x)=\left| \begin{matrix}    x & 1+\sin x & \cos x  \\    1 & \log (1+x) & 2  \\    {{x}^{2}} & 1+{{x}^{2}} & 0  \\ \end{matrix} \right|\] \[=x\{-2(1+{{x}^{2}})\}-(1+\sin x)(-2{{x}^{2}})\] \[+\cos \{1+{{x}^{2}}-{{x}^{2}}\log (1+x)\}\] \[=-2x-2{{x}^{3}}+2{{x}^{2}}+2{{x}^{2}}\sin x\] \[+\cos x\{1+{{x}^{2}}-{{x}^{2}}\log (1+x)\}\] \[\therefore \]Coefficient of\[x\]in\[f(x)=-2\]


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