Check 1 - checked
Check 2 - unchecked
Check 3 - checked
Check 4 - unchecked
Check 5 - checked

$('input[name="thename"]').prop('checked', true);

$('input[name="thename"]').filter(':eq(0), :eq(2), :eq(4)').prop('checked', true);

<input type='checkbox' name='name' id='cb_1'/>
<input type='checkbox' name='name' id='cb_2'/>
<input type='checkbox' name='name' id='cb_3'/>
<input type='checkbox' name='name' id='cb_4'/>
<input type='checkbox' name='name' id='cb_5'/>

1 <input type='checkbox' name='my_name' /><br>
2 <input type='checkbox' name='my_name' /><br>
3 <input type='checkbox' name='my_name' /><br>
4 <input type='checkbox' name='my_name' /><br>
5 <input type='checkbox' name='my_name' /><br>
    <script type="text/javascript">​
        // Event handler activates when value of input with specified name is changed
        $("input[name=my_name]").on("change", function(event) {
            // checks if checkbox was checked, if so - deletes it
            if (true === $(this).prop('checked')) $(this).remove();
        });​
    </script>