The number of four letter words that can be formed using letters of the word BARRACK

Number of different nine digit numbers, that can be formed from the digits in the number 223355888 by rearranging its digits, so that the odd digits occupy even positions, is

If 3 books on Physics, 2 books on Chemistry and 4 books on Mathematics are to be arranged on a shelf so that all the Physics books are together and all the Mathematics books are together, then the number of such arrangements is

If in a regular polygon, the number of diagonals are 54, then the number of sides of the polygon are