If $33!$ is divisible by $2^n$,where $n \in N$,then the sum of all possible values of $n$ is:

In how many ways can $6$ apples be distributed among $3$ boys,there being no restriction to the number of apples each boy may get?

There are $m$ points on a straight line $AB$ and $n$ points on another line $AC$,none of them being the point $A$. Triangles are formed from these points as vertices when $(i)$ $A$ is excluded and $(ii)$ $A$ is included. Then the ratio of the number of triangles in the two cases is

All the five-digit numbers in which each successive digit exceeds its predecessor are arranged in the increasing order of their magnitude. The $97^{th}$ number in the list does not contain the digit:

The number of times the digit $5$ will be written when listing the integers from $1$ to $1000$ is

The number of ways in which $5$ boys and $3$ girls can be seated on a round table if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other,is