Ajax implementation

Hello Friends,
I trying to ajax Implementation :

Here , i try

1) make template where having dropdown of parent category when we select it , it will show you child category in disbaled dropdown.

create template having code below :

<?php wp_dropdown_categories('show_count=5&selected=-1&hierarchical=1&depth=1&hide_empty=0&exclude=1&show_option_none=Main Categories&name=main_cat')?>

header file have added jquery :

[Code moderated as per the Forum Rules. Please use the pastebin]

but it not works anyone please help. . .