append options and set value code example

Example 1: To append dropdown option using jquery

$('#ddlGroup').append(new Option('Select group', '0'));

Example 2: Appending the option element using jquery each function

Here , object contains the list of values

$.each(obj , function (key, value) {
                                $('#GroupName').append($('<option>',
                                    {
                                    value: value.id,
                                    text: value.Group_Name
                                }));