The number of 5-digit numbers consisting of distinct digits that can be formed such that only odd digits occur at odd places is

There are 10 points in the plane, of which 5 points are collinear and no three among the remaining are collinear. Then the number of distinct straight lines that can be formed out of these 10 points is

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

Consider an $8 \times 8$ chessboard. The number of ways 8 rooks can be placed on the board such that no two rooks are in the same row and no two are in the same column is

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 integers greater than 5000 and divisible by 5 that can be formed with the digits 1, 3, 5, 7, 8, 9 where no digit is repeated is

The number of ways in which coins of denominations of rupees 2, 5 and, 10 can be combined to make a value of rupees 50 is