How many words can be formed using the letters of the word $BHARAT$ such that $B$ and $H$ never come together?

The number of distinct positive integers that can be formed using $0, 1, 2, 3$,where each integer is used at most once,is equal to

Numbers greater than $1000$ but not greater than $4000$ which can be formed with the digits $0, 1, 2, 3, 4$ (repetition of digits is allowed),are

All the letters of the word $ABRACADABRA$ are arranged in different possible ways. The number of such arrangements in which the vowels are together is:

In a class of $20$ students,in how many ways can the following prizes be awarded?
If the first and second prizes are for Mathematics,the first and second prizes for Physics,the first prize for Chemistry,and the first prize for English are to be awarded.

If all possible numbers are formed by using the digits $1, 2, 3, 5, 7$ without repetition and they are arranged in descending order,then the rank of the number $327$ is