Previous Year Paper
CAT2004Previous Years Paper
N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a twomin song, one pair after the other. If the total time taken for singing is 28 min, what is N?
A  5 
B  7

C  9 
D  None of the above

Each person will form a pair with all other persons except the two beside him. Hence, he will form (n – 3) pairs.
If we consider each person, total pairs = n(n − 3) but here each pair is counted twice.
Hence, the actual number of pairs =
They will sing for × 2 = n(n−3) min
Hence, n (n−3) = 28
⇒ n^{2}– 3n – 28 = 0
⇒ n = 7 or −4
Discarding the –ve value: n = 7
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