In how many ways can a team of $3$ boys and $3$ girls be selected from $5$ boys and $4$ girls?

If $^nC_4, ^nC_5,$ and $^nC_6$ are in $A.P.,$ then $n$ can be

If $^{n-1}C_r = (k^2 - 3) \cdot ^nC_{r+1}$,then an interval containing the values of $k$ is

The number of all possible ways of distributing $8$ identical apples among $3$ persons is

The number of $4$-letter words,with or without meaning,each consisting of $2$ vowels and $2$ consonants,which can be formed from the letters of the word $UNIVERSE$ without repetition is $.........$.

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