keep the selected value on page load jquery code example

Example 1: how to fetch the selected value of dropdown jquery

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$('#ddlName option:selected').val();

Example 2: jquery dropdown selected value show field

jQuery(document).ready(function() {
    jQuery("#carm3").change(function() {
        if (jQuery(this).val() === 'other'){ 
            jQuery('input[name=other_interest]').show();   
        } else {
            jQuery('input[name=other_interest]').hide(); 
        }
    });
});