Question

Assertion :$(n\ge 3)$ for $n$ cirlces the value of $n$ for which the number of radical axis is equal to the number of radical centre is $5$. Reason: If no two of $n$ circles are concentric. No three of the centre are collinear then number of radical centres is $\frac{n(n-1)(n-2)}{3!}$.

• 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. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

We know, number.of radical centres $=$ Number of radical axis
${\Rightarrow }^n{C}_3{=}^n{C}_2$
${\Rightarrow }^n{C}_{n-3}{=}^n{C}_2$
$\Rightarrow n=5$, (using ${}^n{C}_x{=}^n{C}_y$ then
$x+y=n$ )
Hence choice (a) is correct answer.