JEE Advanced 2014 · Paper 1 · Mathematics Q52

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MathematicsInteger+3Question 52 of 60

Let $n\ge2$ be an integer. Take $n$ distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of $n$ is

Your answer

Answer and worked solution

Official answer: 5

Counts. There are $\binom n2$ segments. Adjacent pairs on the circle form $n$ sides, coloured blue; the remaining $\binom n2-n$ are red.

Equal.
$\binom n2-n=n\implies\frac{n(n-1)}2=2n\implies n-1=4\implies n=5.$

Answer: 5

Topics:Combinations

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JEE Advanced 2014 · Paper 1, Mathematics question 52