Question

The maximum possible number of points of intersection of 7 straight lines and 5 circles is:

• A. 111
• B. 109
• C. 107
• D. 105

Answer 1

Answer: (A)

Solution: Maximum possible number of points of intersection of 7 lines is ${}^7{C}_2=21$.
Maximum possible number of points of intersection of 5 circles in $2\left({}^5{C}_2\right)=20$
[ $\because$ two circles can intersect in two distinct points.]
Maximum possible number of points of intersection of 5 circles and 7 lines is $2(5)(7)=70$
Thus, maximum possible number of points of intersection is
$21+20+70=111$