Previous Year Paper
CAT-2004-Previous 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 two-min song, one pair after the other. If the total time taken for singing is 28 min, what is N?
|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
⇒ n2– 3n – 28 = 0
⇒ n = 7 or −4
Discarding the –ve value: n = 7