JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Expansion of determinants, Solution of equation in the form of determinants and properties of determinants

  • question_answer
    \[\left| \,\begin{matrix}    {{\sin }^{2}}x & {{\cos }^{2}}x & 1  \\    {{\cos }^{2}}x & {{\sin }^{2}}x & 1  \\    -10 & 12 & 2  \\ \end{matrix}\, \right|=\] [EAMCET 1994]

    A) 0

    B) \[12{{\cos }^{2}}x-10{{\sin }^{2}}x\]

    C) \[12{{\sin }^{2}}x-10{{\cos }^{2}}x-2\]

    D) \[10\sin 2x\]

    Correct Answer: A

    Solution :

    Applying\[{{C}_{1}}\to {{C}_{1}}+{{C}_{2}}\], we get\[\left| \,\begin{matrix}    1 & {{\cos }^{2}}x & 1  \\    1 & {{\sin }^{2}}x & 1  \\    2 & 12 & 2  \\ \end{matrix}\, \right|\,=0\].


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