How many permutations can be formed from the letters of the word $ALGEBRA$ without changing the relative positions of the vowels and consonants?

How many numbers greater than $1000000$ can be formed by using the digits $1, 2, 0, 2, 4, 2, 4$?

Seven scientists $S_1, S_2, \ldots, S_7$ are invited to deliver one lecture each in a conference. The number of ways all the seven lectures can be arranged such that the lecture of $S_1$ is prior to that of $S_3$ and the lecture of $S_3$ is prior to that of $S_7$ is

How many words of $4$ distinct letters can be formed using the letters of the word $DHOLPUR$ if $L$ and $P$ are always excluded?

How many numbers between $3000$ and $4000$ can be formed using the digits $3, 4, 5, 6, 7, 8$ without repetition,such that the numbers are divisible by $5$?

The number of ways in which $6$ boys and $4$ girls can be arranged in a row such that between any two girls there must be exactly $2$ boys is