IPMAT Indore (MCQ) PYQs

In a chess tournament, there are four groups, each containing an equal number of players. Each player plays

1. against every other player belonging to one's own group exactly once;
2. against each player belonging to one of the remaining three groups exactly twice;
3. against each player belonging to one of the remaining two groups exactly three times; and
4. against each player belonging to the remaining group exactly four times.

If there are more than 1000 matches being played in the tournament, the minimum possible number of players in each group is

The number of values of $x$ for which $C \binom {17-x}{3x+1}$ is defined as an integer is

In how many ways can the letters of the word MANAGEMENT be arranged such that no two vowels appear together?