If you want to remove the first option use this
$(document).ready(function() { $("#q_c_0_a_0_name").children().first().remove(); });
If you want to remove the first option after clicking on the select box use this
$(document).ready(function() { var removed=false; $(document).on("click","select",function() { if(!removed) { $(this).children().first().remove(); removed=true; } }); });

If you want to remove the first option use this
$(document).ready(function() { $("select").children().first().remove(); });
If you want to remove the first option after clicking on the select box use this
$(document).ready(function() { var removed=false; $(document).on("click","select",function() { if(!removed) { $(this).children().first().remove(); removed=true; }

}); });