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J & K CET Engineering J and K - CET Engineering Solved Paper-2012

  • question_answer
    The points \[(a,\,\,0),\,\,\,(0,\,\,b)\] and \[(1,\,\,-1)\] are collinear \[(a\ne 0,\,b\ne 0),\] if

    A)  \[b-a=ab\]

    B)  \[b+a=ab\]

    C)  \[a-b=ab\]      

    D)  \[a+b=-ab\]

    Correct Answer: A

    Solution :

    Since, points \[(a,\,0),\,\,(0,b)\] and  \[(1,-1)\] are collinear. \[\therefore \] \[\left| \begin{matrix}    a & 0 & 1  \\    0 & b & 1  \\    1 & -1 & 1  \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[a(b+1)+0+1(0-b)=0\] \[\Rightarrow \] \[ab+a-b=0\] \[\Rightarrow \] \[b-a=ab\]


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