Find how many words can be formed out of the letters of the word '$ORIENTAL$' so that vowels always occupy the odd places.

The digits $4, 5, 6, 7, 8$ are written in every possible order. The number of numbers greater than $56000$ is

The sum of the digits in the unit place of all numbers formed with the help of $3, 4, 5, 6$ taken all at a time is

$3$ boys $B_1, B_2, B_3$ and $6$ girls $G_1, G_2, . . . , G_6$ are to be seated in a row. The number of ways they can be seated such that $B_1, B_2$ are separated and $G_1, G_2$ are also separated is equal to:

$A$ student is allowed to select at most $n$ books from a collection of $(2n + 1)$ books. If the total number of ways in which he can select at least one book is $63$,then the value of $n$ is

$A$ number lock consists of three rings. If the $1^{st}$ ring is marked with digits $0$ to $9$,the $2^{nd}$ ring is marked with prime numbers greater than $2$ but less than $30$,and the $3^{rd}$ ring is marked with all vowels,find the total number of unsuccessful attempts.