The sum of all the $4$-digit numbers formed by taking all the digits from ${0, 3, 6, 9}$ without repetition is

There are $5$ volumes of Mathematics among $25$ books. They are arranged on a shelf in random order. The probability that the volumes of Mathematics stand in increasing order from left to right (the volumes are not necessarily kept side by side) is

Let $n = 1! + 4! + 7! + \ldots + 400!$. Then the ten's digit of $n$ is

If $8 \cdot {}^{7}P_{r} = 7 \cdot {}^{8}P_{r-1}$,what is the value of $r$?

$6$ different letters of an alphabet are given. Words with $4$ letters are formed from these given letters. The number of words which have at least one letter repeated and no two same letters are together is:

The number of ways $5$ boys and $4$ girls can sit in a row so that either all the boys sit together or no two boys sit together,is $......$