The remainder obtained when $1! + 2! + 3! + \dots + 11!$ is divided by $12$ is

The number of different words that can be formed using all the letters of the word $APPLICATION$ such that no two vowels come together is -

If the number of circular permutations of $9$ distinct things taken $5$ at a time is $n_1$ and the number of linear permutations of $8$ distinct things taken $4$ at a time is $n_2$,then $\frac{n_1}{n_2}=$

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

There are $15$ stations on a train route and the train has to be stopped at exactly $5$ stations among these $15$ stations. If it stops at at least two consecutive stations,then the number of ways in which the train can be stopped is

The number of different words that can be formed from the letters of the word $SUCCESS$ in which the two $C$ are together but no two $S$ are together are: