JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

  • 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 :

    [a] 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. therefor 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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