What you are looking to do could be accomplished 2 ways I can think of off the top of my head.
First, Capture the change event for all input items in your form individually
$("#search_options input,#search_options select").change(function() {
// "this" is the input that has changed so you would check if it had id = "project_category" here
});
Alternatively you could track the current value of the "project_category" on every change
var current_Project_Category = "";
$("#search_options").change(function() {
if(current_Project_Category != $(this).find("#project_category").val())
{
//project category has changed so mark this as the current one
//also run any change code here
current_Project_Category = $(this).find("#project_category").val()
}
});