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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Self Evaluation Test - Determinats

  • question_answer
    If [ ] denotes the greatest integer less than or equal to the real number under consideration and \[-1\le x<0;\] \[0\le y<1;\] \[1\le z<2,\] then the value of the determinant\[\left| \begin{matrix}    [x]+1 & [y] & [z]  \\    [x] & [y]+1 & [z]  \\    [x] & [y] & [z]+1  \\ \end{matrix} \right|\]is

    A) \[[z]\]

    B) \[[y]\]

    C) [x]

    D) None of these

    Correct Answer: A

    Solution :

    [a] Since,  \[-1<x<0\]     \[\therefore \,\,\,\,[x]=-1\] \[0<y<1\,\,\,\,\,\,\,\,\,\,\,\therefore \,\,[y]=0,\] \[1<z<2\,\,\,\,\,\,\,\,\,\,\therefore \,[z]=1\] \[\therefore \] Given determinant \[=\left| \begin{matrix}    0 & 0 & 1  \\    -1 & 1 & 1  \\    -1 & 0 & 2  \\ \end{matrix} \right|=1=[z]\]


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