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:

If $\binom{189}{35} + \binom{189}{x} = \binom{190}{x}$,then $x = \dots$

If ${}^nC_4, {}^nC_5$ and ${}^nC_6$ are in $A.P.$, then $n$ is

There are $5$ apples,$4$ mangoes,$3$ oranges,and $1$ each of $2$ other varieties of fruits. The number of ways of selecting at least one fruit of each kind is

If ${ }^{n} C_{12}={ }^{n} C_{8}$,then $n$ is equal to

There are $6$ different novels and $3$ different poetry books on a table. If $4$ novels and $1$ poetry book are to be selected and arranged in a row on a shelf such that the poetry book is always in the middle,then the number of such possible arrangements is