Hello @kartik,
Use $.ajax to call a server context (or URL, or whatever) to invoke a particular 'action'. What you want is something like:
$.ajax({ url: '/my/site',
         data: {action: 'test'},
         type: 'post',
         success: function(output) {
                      alert(output);
                  }
});
On the server side, the action POST parameter should be read and the corresponding value should point to the method to invoke, e.g.:
if(isset($_POST['action']) && !empty($_POST['action'])) {
    $action = $_POST['action'];
    switch($action) {
        case 'test' : test();break;
        case 'blah' : blah();break;
        // ...etc...
    }
}
Hope it helps!!
Thank You!!