How many such letters are there in the word category each of which is as far away from tha beginning of the word as they are arranged in alphabetical order?

Well, honey, in the Word "category," there are two letters that fit your fancy: "A" and "G." Both of these sassy letters are as far away from the beginning of the Word as their alphabetical order. So, go ahead and give those two letters a round of applause for being alphabetically awesome.