Add option to html dropdownlist with jQuery

$('#dropdownId').append($('<option>', {
                    value: value,
                    text: text ,
                    selected: true
}));

// Not selected option 

$('#dropdownId').append($('<option>', {
                    value: value,
                    text: text                  
}));

Set a html checkbox to indeterminate state

var checkbox = document.getElementById('myCheckbox');
checkbox.indeterminate = true;