The total number of natural numbers of six digits that can be made with digits $1, 2, 3, 4$,if all digits are to appear in the same number at least once,is

$A$ string of letters is to be formed by using $4$ letters from all the letters of the word "$MATHEMATICS$". The number of ways this can be done such that two letters are of the same kind and the other two are of a different kind is:

If $a + b + c = 50$ and $a, b, c$ are non-negative even integers,then the greatest value of $ab^2c$ is:

If $n$ is an integer with $0 \leq n \leq 11$,then the minimum value of $n!(11-n)!$ is attained when a value of $n$ equals to

For all $n \in N$,the product $(n+24)(n+25)(n+26)(n+27)$ is always divisible by:

The number of $6$-letter words,with or without meaning,that can be formed using the letters of the word $\text{MATHS}$ such that any letter that appears in the word must appear at least twice,is $...$