how to select and deselect all options in a select box

You need to add the multiple attribute to the select element, and then you can:

$('#selectall').click(function() {
    $('select#studentremain option').attr("selected","selected");
});   

$('#deselectall').click(function() {
    $('select#studentremain option').removeAttr("selected");
});

Try this demo

Must add multiple="multiple" in select element

HTML:

<select multiple="multiple" name="remaintextarea" id="studentremain" size="10">
    <option value="one">One</option>
    <option value="two">Two</option>
    <option value="three">Three</option>
</select>
<button type='button' id='selectall'>Select All</button>
<button type='button' id='deselectall'>De-Select All</button>

JS:

$('#selectall').click(function() {
    $('#studentremain > option').attr("selected", "selected");
});   

$('#deselectall').click(function() {
    $('#studentremain > option').removeAttr("selected");
});

Somehow the answers above did not work for me. Seems that you have to use properties instead of attributes. Here is the code:

$('#selectall').click(function() {
    $('select#studentremain option').prop("selected",true);
});   

$('#deselectall').click(function() {
    $('select#studentremain option').prop("selected",false);
});

Documentation says that selected attribute only specifies that an option should be pre-selected when the page loads. But is not set when the actual option is selected by the user. Source