Is there any way to check reachability test of server in jQuery

To test if your server is up you will need to connect to it and check status massage:

$.ajax('LINK GOES HERE', {
  statusCode: {
    404: function() {
      alert('Not working');
    },
    200: function() {
      alert('Working');
    }
  }
});

Working jsFiddle example: http://jsfiddle.net/Gajotres/PMrDn/47/

$.ajax({url: "http://api.themoviedb.org/2.1/Movie.search/en/json/23afca60ebf72f8d88cdcae2c4f31866/The Goonies",
        dataType: "jsonp",
        statusCode: {
            200: function (response) {
                alert('status 200');
            },
            404: function (response) {
                alert('status  404 ');
            }
        }                        
 });

EDIT :

Use this:

$.ajax({url: "http://192.168.12.171",
        type: "HEAD",
        timeout:1000,
        statusCode: {
            200: function (response) {
                alert('Working!');
            },
            400: function (response) {
                alert('Not working!');
            },
            0: function (response) {
                alert('Not working!');
            }              
        }
 });

Working example: http://jsfiddle.net/Gajotres/PMrDn/48/