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JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Geometrical Problems

  • question_answer
    In a plane there are 37 straight lines of which 13 pass through the point \[A\] and 11 pass through the point \[B\]. Besides no three lines pass through one point, no line passes through both points \[A\]and \[B\] and no two are parallel. Then the number of intersection points the lines have is equal to

    A) 535

    B) 601

    C) 728

    D) None of these

    Correct Answer: A

    Solution :

    The number of points of intersection of 37 straight lines is\[^{37}{{C}_{2}}\]. But 13 of them pass through the point\[A\]. Therefore instead of getting \[^{13}{{C}_{2}}\] points we get merely one point. Similarly 11 straight lines out of the given 37 straight lines intersect at\[B\]. Therefore instead of getting \[^{11}{{C}_{2}}\] points, we get only one point. Hence the number of intersection points of the lines is\[^{37}{{C}_{2}}{{-}^{13}}{{C}_{2}}{{-}^{11}}{{C}_{2}}+2=535\].


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