Edit in JSFiddle

$(document).ready(function(){
    $('#btnRemoveSel').click(function(){
       $('#ddlList option:selected').remove();
    });
    
    $('#btnRemoveByVal').click(function(){
      $('#ddlList option[value="3"]').remove();
    });
    
     $('#btnRemoveByText').click(function(){
         $('#ddlList option:contains("HTML")').remove();
    });
        
    $('#btnRemoveAllExceptFirst').click(function(){
       $('#ddlAnotherList option:not(:first)').remove();  
    });
    
    $('#btnRemoveAllExceptLast').click(function(){
        $('#ddlRemoveExcludingLast option:not(:last)').remove();
    });
    
    $('#btnRemoveAll').click(function(){  
       $("#ddlRemoveAll").empty();
    });
    
    $('#btnResetPage').click(function(){  
       var options = '<option value="1">ASP.NET</option>' +
                      '<option value="2">C#</option>' +
                      '<option value="3">VB.NET</option>' +
                      '<option value="4">HTML</option>' +
                      '<option value="5">jQuery</option>';
        
         $('select').empty();
         $('select').append(options);
    });
    
});

<select id="ddlList">
  <option value="1">ASP.NET</option>
  <option value="2">C#</option>
  <option value="3">VB.NET</option>
  <option value="4">HTML</option>
  <option value="5">jQuery</option>
</select>

<br/><br/>
<input type="button" id="btnRemoveSel" Value="Remove selected item" />
&nbsp;&nbsp;
<input type="button" id="btnRemoveByVal" Value="Remove Item by Value" />
&nbsp;&nbsp;
<input type="button" id="btnRemoveByText" Value="Remove Item by Text" />
<br/><br/>

<select id="ddlAnotherList">
  <option value="1">ASP.NET</option>
  <option value="2">C#</option>
  <option value="3">VB.NET</option>
  <option value="4">HTML</option>
  <option value="5">jQuery</option>
</select>

<input type="button" id="btnRemoveAllExceptFirst" Value="Remove all items excluding first item" /> 
<br/><br/>
<select id="ddlRemoveExcludingLast">
  <option value="1">ASP.NET</option>
  <option value="2">C#</option>
  <option value="3">VB.NET</option>
  <option value="4">HTML</option>
  <option value="5">jQuery</option>
</select>
<input type="button" id="btnRemoveAllExceptLast" Value="Remove all items excluding Last item" />
<br/><br/>
<select id="ddlRemoveAll">
  <option value="1">ASP.NET</option>
  <option value="2">C#</option>
  <option value="3">VB.NET</option>
  <option value="4">HTML</option>
  <option value="5">jQuery</option>
</select>


<input type="button" id="btnRemoveAll" Value="Remove All" />
&nbsp;&nbsp;

<br/><br/><br/>

<input type="button" id="btnResetPage" Value="Reset All" />