@Html.DropDownListFor(x => x.StudentId, Enumerable.Empty<SelectListItem>(),
    new { style ="width: 100%;" } )

$("#StudentId").select2({
   multiple: false,
   placeholder: "Select",
   allowClear: true,
   tags: true,

   ajax: {
       url: '/Grade/StudentLookup',
       dataType: 'json',
       delay: 250,

       data: function (params) {
           return {
               //q: params.Name, // search term
               //page: params.page
               query : 'test' //this parameter can be passed via AJAX
               //!!! but I cannot get the selected text or value of dropdownlist
           };
       },

       processResults: function (data, page) {
           var newData = [];
           $.each(data, function (index, item) {
               newData.push({
                   id: item.Id,     //id part present in data
                   text: item.Name  //string to be displayed
               });
           });
           return { results: newData };
       },
       cache: true
   },
   escapeMarkup: function (markup) { return markup; }, // let our custom formatter work
   minimumInputLength: 0, //for listing all, set : 0
   maximumInputLength: 20, // only allow terms up to 20 characters long
});