Resolve into partial factors:\(\frac { x+4 }{ ({ x }^{ 2 }-4)(x+1) } \)

Solve : \(\frac { (2x+1)! }{ (x+2)! } .\frac { (x-1)! }{ (2x-1)! } =\frac { 3 }{ 5 } \)

How may different numbers between 100 and 1000 can be formed using the digits 0, 1,2,3,4, 5, 6 assuming that in any number, the digits are not repeated.

It the letters of the word are arranged as in dictionary, find the rank of the word "AGAIN".

There are 6 gentlemen and 4 ladies to line at a round table. In how many ways can they seat themselves so that no two ladies together?