On Click of Jquery Tab, bind data to the drop down list from database

1) So basically for each tab subscribe on a click.
On tab click event handler you can reach to sender property which is actually the tab object.

Within this tab navigate (find) drop down list with usage of:

var dropDowm = $("#nameOfYourDropDown");

Then you might need to get some data from Web-service by requesting it with help of either $.Ajax or $.getJson methods.
In core of web-service i can advise to you to use either REST WCF or ASP.NET WebApi, by reason, that they use lighweight messaging pattern.

$.ajax({type:"GET",url:"http://somelink/getdata?parameter=paramvalue",
success:function(jsonStr){
//do some stuff for populate drop box here.....
}}