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JEE Main & Advanced Mathematics Straight Line Question Bank Critical Thinking

  • question_answer
    Given the four lines with equations \[x+2y=3,\] \[3x+4y=7,\,\,2x+3y=4\,\,\] and \[4x+5y=6,\] then these lines are [IIT 1980; Pb. CET 2003]

    A)            Concurrent                                

    B)            Perpendicular

    C)            The sides of a rectangle           

    D)            None of these

    Correct Answer: D

    Solution :

               These lines cannot be the sides of a rectangle as none of these are parallel nor they are perpendicular.                    Now check concurrency                    \[\left| \,\begin{matrix}    1 & 2 & -3  \\    3 & 4 & -7  \\    2 & 3 & -4  \\ \end{matrix}\, \right|=1(-16+21)-2(2)-3(1)\ne 0\]                    Hence neither concurrent.


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