MVC Api Controllers (Get/ Post)

System.Web.Http.ApiController is one of the controller types in Asp MVC

Default Routing

routes.MapHttpRoute(
    name: "DefaultApi",
    routeTemplate: "api/{controller}/{id}",
    defaults: new { id = RouteParameter.Optional }
);

Any request method like Get, Post, Put, etc can be used with action names started with the method name
ex:
GetEmployees()
GetProducts()

but it checks the input parameters if we use more than one Get or other method names.

When posting  to an action like below
public HttpResponseMessage PostApplication(Application_ui param)

public class Application_ui{
 public string Action{get;set;};
 public int No{get;set;}
}

you should have a class that can be instantiate in parameter and the client side call should match the object properties
if you use json again that should be stringified
$.post("/api/ApplicationAPI/", JSON.stringify({Action:'add', No:'34'}));

Reference
http://www.asp.net/web-api/overview/working-with-http/sending-html-form-data,-part-1#sending_simple_types
http://www.asp.net/web-api/overview/web-api-routing-and-actions/routing-and-action-selection