1

In a tournament, there are n teams T1, T2,.............,Tn, with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common T1 and T2, T2 and T3, . . . , Tn-1 and Tn, and Tn and T1. No other pair of teams has any player in common. How many players are participating in the tournament, considering all the n teams together ?

In a tournament, there are n teams T1, T2,.............,Tn, with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common T1 and T2, T2 and T3, . . . , Tn-1 and Tn, and Tn and T1.

No other pair of teams has any player in common. How many players are participating in the tournament, considering all the n teams together ?

2

Ten years ago, the ages of the members of a joint family of eight people added up to 231 yr. Three years later, one member died at the age of 60 yr and a child was born during the same year. After another three years, one more member died, again at 60 and a child was born during the same year. The current average age of this eight-member joint family is nearest to....

3

The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10n, on the nth day of 2OO7 (n = 1, 2, ..., 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n, on the nth day of 2007 (n =1, 2, .., 365). On which date in 2007 will the prices of these two varieties of tea be equal ?

4

Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you pay a bill of 107 Misos ?

5

A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees instead of paise and paise instead of rupees. After buyng a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque. Which of the following is a valid statement about the cheque amount ?

6

How many pairs of positive integer’s m, n satisfy (1 / m) + (4 /n) = (1 /12), where n is an odd integer less than 60 ?

How many pairs of positive integer’s m, n satisfy

(1 / m) + (4 /n) = (1 /12), where n is an odd integer less than 60 ?

7

Which among 2^{1/2}, 3^{1/3}, 4 ^{1/4}, 6^{1/6} and, 12^{1/12} is the largest ?

8

Consider a sequence where the nth term, tn = n / (n + 2), n =1, 2,... . The value of t3 x t4 x t5 x ... x t53 equals

9

If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, then what is the value of abc/def?

10

If x = -0.5, then which of the following has the smallest value?

and Test