Question

Assertion :The maximum number of points of intersection of $8$ circles of unequal radii is $56$. Reason: The maximum number of points into which $4$ circles of unequal radii and $4$ non coincident straight lines intersect, is $50$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Two circles intersect at maximum $2$ points.
$\therefore$ Maximum number of points of intersection
$=2\times$number of selections of two circles from $8$ circles
$2\times {}^8{C}_2=2\times 28=56$
Statement 2 :

$4$ lines intersect each other in ${}^4{C}_2=6$ points
$4$ circles intersect each other in $2\times {}^4{C}_2=12$ points
Further, one lines and one circle intersect in two points.

So $4$ lines will intersect four circles in $32$ points.
Maximum number of points $=6+12+32=50$

Hence, both assertion and reason are correct but reason is not the correct explanation for assertion.