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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2015

  • question_answer
    Matrix \[a=\frac{F-({{m}_{1}}+{{m}_{2}}+{{m}_{3}})g\,\sin \theta }{({{m}_{1}}+{{m}_{2}}+{{m}_{3}})}\]is invertible for

    A) \[{{m}_{3}}\]                     

    B) \[N-{{m}_{3}}\,\,g\sin \theta ={{m}_{3}}a\]

    C) Both (a) and (b)               

    D) None of these

    Correct Answer: D

    Solution :

    Since, A is invertible matrix. \[\therefore \]                  \[|A|\ne 0\] \[\Rightarrow \]               \[\left| \begin{matrix}    1 & 0 & -k  \\    2 & 1 & 3  \\    k & 0 & 1  \\ \end{matrix} \right|\ne 0\] \[\Rightarrow \]               \[1(1-0)+k(0-k)\ne 0\] \[\Rightarrow \]               \[1-{{k}^{2}}\ne 0\] \[\Rightarrow \]               \[k\ne \pm 1\]


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