JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Mock Test - Permutations and Combinations

  • question_answer
    The maximum number of points of intersection of five lines and four circles is

    A) 60                    

    B) 72

    C) 62                   

    D) none of these

    Correct Answer: C

    Solution :

    [c] Two circles intersect at two distinct points. Two straight lines intersect at one point. One circle and one straight line intersect at two distinct points. Then the total numbers of points of intersections are as follows;
    Number of ways of selection Points of intersection
    Two straight lines: \[^{5}{{C}_{2}}\] \[^{5}{{C}_{2}}\times 1=10\]
    Two circles: \[^{4}{{C}_{2}}\] \[^{4}{{C}_{2}}\times 2=12\]
    One line and circle: \[^{5}{{C}_{1}}{{\times }^{4}}{{C}_{1}}\] \[^{5}{{C}_{1}}{{\times }^{4}}{{C}_{1}}\times 2=40\]
    Total 62

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