The remainder of $n^4-2n^3-n^2+2n-26$ when divided by $24$ is:

If ${}^n P_r = 30240$ and ${}^n C_r = 252$,then the ordered pair $(n, r)$ is equal to

The students $S_{1}, S_{2}, \ldots, S_{10}$ are to be divided into $3$ groups $A, B$ and $C$ such that each group has at least one student and the group $C$ has at most $3$ students. Then the total number of possibilities of forming such groups is ........ .

$A$ five-digit number divisible by $3$ is to be formed using the digits $0, 1, 2, 3, 4, 5$ without repetition. The total number of ways this can be done is:

There are three sections in a question paper,each section containing $4$ questions. If a candidate has to answer exactly $5$ questions from this paper such that at least one question is answered from each section,then the number of ways in which a candidate can make the choice of questions is

How many numbers can be formed from the digits $1, 2, 3, 4$ when repetition is not allowed?