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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
    Solution of the equation \[\left| \,\begin{matrix}    1 & 1 & x  \\    p+1 & p+1 & p+x  \\    3 & x+1 & x+2  \\ \end{matrix}\, \right|=0\]are [AMU 2002]

    A) \[x=1,\,2\]

    B) \[x=2,\,3\]

    C) \[x=1,\,p,\,2\]

    D) \[x=1,\,2,\,-p\]

    Correct Answer: A

    Solution :

    \[A=\left| \begin{matrix}    1 & 1 & x  \\    p+1 & p+1 & p+x  \\    3 & x+1 & x+2  \\ \end{matrix}\, \right|\] \[|A|\,=0\,\text{for}\,x=1\,\text{ and }2\]. So option (a) is correct.


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