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
    \[\left| \,\begin{matrix}    1 & 5 & \pi   \\    {{\log }_{e}}e & 5 & \sqrt{5}  \\    {{\log }_{10}}10 & 5 & e  \\ \end{matrix}\, \right|=\]

    A) \[\sqrt{\pi }\]

    B) e

    C) 1

    D) 0

    Correct Answer: D

    Solution :

    \[\Delta =\left| \,\begin{matrix}    1 & 5 & \pi   \\    1 & 5 & \sqrt{5}  \\    1 & 5 & e  \\ \end{matrix}\, \right|\,=0\] \[(\because \,\,{{\log }_{a}}a=1\text{ and }5{{C}_{1}}\equiv {{C}_{2}})\]


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