IPMAT Indore (MCQ) PYQs

How many different numbers can be formed by using only the digits 1 and 3 which are smaller than 3000000?

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 triangles that can be formed by choosing points from 7 points on a line and 5 points on another parallel line is _________.