The largest $n \in N$ for which $7^n$ divides $101!$ is:

All the letters of the word $ANIMAL$ are permuted in all possible ways and the permutations thus formed are arranged in dictionary order. If the rank of the word $ANIMAL$ is $x$,then the permutation with rank $x$,among the permutations obtained by permuting the letters of the word $PERSON$ and arranging the permutations thus formed in dictionary order is

$n$ objects are distributed at random among $n$ persons. The number of ways in which this can be done so that at least one of them will not get any object is

An envelope has space for at most $3$ stamps. If you are given three stamps of denomination $1$ and three stamps of denomination $a$ (where $a > 1$),what is the least positive integer for which there is no possible stamp value?

If $f(n) = n! (31-n)!$,where $n \in \{0, 1, 2, \ldots, 31\}$,then the minimum value of $f(n)$ is

For a set of $5$ true or false questions,no student has written all the 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