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  • The maximum number of intersections between 15 straight lines and 11 circles isOption: 1 430O

The maximum number of intersections between 15 straight lines and 11 circles is

Option: 1

430


Option: 2

330


Option: 3

490


Option: 4

390


Answers (1)

best_answer

Given that,

There are 15 straight lines and 11 circles.

The point of intersection between 2 lines is given by,

\mathrm{\begin{aligned} &{ }^{15} C_2=\frac{15 !}{2 ! 13 !}\\ &{ }^{15} C_2=\frac{15 \times 14}{2}\\ &{ }^{15} C_2=105 \end{aligned}}

The point of intersection between 2 circles is given by,

\mathrm{ { }^{11} C_2=\frac{11 !}{2 ! 9 !} }

\mathrm{ { }^{11} C_2=\frac{11 \times 10}{2}}

\mathrm{ { }^{11} C_2=55}

The point of intersection between 1 line and 1 circle is given by,

\mathrm{\begin{aligned} &{ }^{15} C_1 \times{ }^{11} C_1 \times 2=15 \times 11 \times 2\\ &{ }^{15} C_1 \times{ }^{11} C_1 \times 2=330 \end{aligned}}

Therefore, the total number of points of intersection is 105 + 55 + 330 = 490.

 

 

 

Posted by

Suraj Bhandari

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