A group consists of 8 boys and 5 girls, then the number of committees of 5 persons that can be formed, if committee consists of at least 2 girls and at most 2 boys, are

A linguistic club of a certain Institute consists of 6 girls and 4 boys. A team of 4 members to be selected from this group including the selection of a Captain (from among these 4 members) for the team. If the team has to include atmost one boy, the number of ways of selecting the team is

If at the end of certain meeting, everyone had shaken hands with everyone else, it was found that 45 handshakes were exchanged, then the number of members present at the meeting, are

For a set of five true or false questions, no student has written the all correct answers and no two students have given the same sequence of answers. The maximum number of students in the class for this to be possible is