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KVPY Sample Paper KVPY Stream-SX Model Paper-6

  • question_answer
    Two dice are rolled to get the coordinates of a point P(x, y) in the Cartesian plane. Find the probability that area of \[\Delta \,PAB\]is 1 sq. unit, where \[A\equiv (1,\,\,1),\]\[B\equiv (2,\,\,0).\] Given that P, A, B lie in anticlockwise order in the plane

    A) \[\frac{1}{6}\]                          

    B) \[\frac{1}{36}\]

    C) \[\frac{1}{12}\]                         

    D) \[\frac{1}{2}\]

    Correct Answer: C

    Solution :

    \[1=\frac{1}{2}\,\,\left| \begin{matrix}    x & y & 1  \\    1 & 1 & 1  \\    2 & 0 & 1  \\ \end{matrix} \right|\]  \[\Rightarrow \] \[x+y=4\]
    \[\therefore \] number of solutions = 3
    \[\therefore \] the required probability\[=\frac{3}{36}=\frac{1}{12}\]


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