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Here , object contains the list of values
$.each(obj , function (key, value) {
$('#GroupName').append($('<option>',
{
value: value.id,
text: value.Group_Name
}));
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//add option to select with jQuery
$('#selectID').append($('<option>', {
value: 1,
text: 'Option Text'
}));
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// Assuming we have a <select> element with id "mySelect"
var mySelect = $("#mySelect");
var option = $("<option>").val("value").text("Option Text");
mySelect.append(option);