As follows:

//Dynamically deletes all options: & NBSP; in the select;  
function delAllOptions(){ 
      document.getElementById("user_dm").options.length=0;  
} 

//Dynamically deletes an option in the select: & NBSP;    
function delOneOption(index){ 
      document.getElementById("user_dm").options.remove(index);  
} 
//Dynamically add option in select :& NBSP;    
function addOneOption(){ 
      //document.getElementById("user_dm").options.add(new Option(2,"mytest"));   

   var selectObj=document.getElementById("user_dm"); 
   alert(selectObj.length); 
   selectObj.options[selectObj.length] = new Option("mytest", "2"); 
}