List of top Mathematics Questions on permutations and combinations asked in MHT CET

If a polygon has 54 diagonals, find the number of sides of the polygon.
The value of \[ {}^{47}C_{4} + \sum_{j=1}^{5} {}^{(52-j)}C_{3} \] is:
\(\int \frac{\cos 2x - \cos 2\alpha}{\cos x - \cos \alpha} dx =\)
The value of \( {}^{47}C_4 + \sum_{j=1}^5 {}^{(52-j)C_3 \) is
There are 6 boys and 4 girls. Arrange their seating arrangement on a round table such that 2 boys and 1 girl can't sit together.

The value of

\[ {}^{47}C_{4} + \sum_{j=1}^{5} {}^{(52-j)}C_{3} \] 

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
If in a regular polygon, the number of diagonals are 54, then the number of sides of the polygon are}
A linguistic club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this group including the selection of a leader (from among these 4 members) for the team. If the team has to include at most one boy, the number of ways of selecting the team is