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JEE Main & Advanced Mathematics Straight Line Question Bank Concurrency of three lines

  • question_answer
    If lines \[4x+3y=1,y=x+5\] and \[5y+bx=3\] are concurrent, then b equals [RPET 1996; MP PET 1997; EAMCET 2003; Pb. CET 2002]

    A)            1     

    B)            3

    C)            6     

    D)            0

    Correct Answer: C

    Solution :

               Lines are concurrent, if \[\left| \,\begin{matrix}    4 & 3 & -1  \\    1 & -1 & 5  \\    b & 5 & -3  \\ \end{matrix} \right|\,=0\]                    Þ  \[4(3-25)-3(-3-5b)-1(5+b)=0\]                    Þ  \[-88+9+15b-5-b=0\Rightarrow -84+14b=0\]                    \ \[b=6\].


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