Answers for "check radio button is selected or not"

check if radio button is checked

$('#element').click(function() {
   if($('#radio_button').is(':checked')) { alert("it's checked"); }
});

check if one of the radio button is checked

if ($('input[name='+ radioName +']:checked').length) {
           // at least one of the radio buttons was checked
           return true; // allow whatever action would normally happen to continue
      }
      else {
           // no radio button was checked
           return false; // stop whatever action would normally happen
      }

radio button not checked

$('input:radio[checked=false]');
this will also work

input:radio:not(:checked)

or

:radio:not(:checked)