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J & K CET Engineering J and K - CET Engineering Solved Paper-2003

  • question_answer
    Given four lines with equations \[x+2y-3=0,\] \[2x+3y-4=0,\] \[3x+4y-5=0,\] \[4x+5y-6=0.\] These lines are

    A)  concurrent

    B)  the sides of quadrilateral

    C)  the sides of a parallelogram

    D)  the sides of a square

    Correct Answer: A

    Solution :

    Given equations of lines are \[x+2y-3=0\]             ...(i) \[2x+3y-4=0\]           ...(ii) \[3x+4y-5=0\]            ...(iii) and        \[4x+5y-6=0\]             ...(iv) On solving Eqs. (i) and (ii), we get \[x=-1,\,\,y=2\] From Eq. (iii), \[3(-1)+4(2)-4=0\] \[\Rightarrow \] \[0=0\] From Eq. (iv), \[4(-1)+5(2)-6=0\] \[\Rightarrow \] \[0=0\] Hence, given lines are concurrent.


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