<?php
    function selected($value, $post) {
        if ($value == $post) {
            return "selected";
        }
    }

    $class= '';
    if (!EMPTY($_POST['class'])) {
        $class = $_POST['class'];
    }
?>

<form action="" method="POST">
    <select name="class">
        <option value="">Please Select</option>
        <option value="nursery1" <?php echo selected($nursery1, $class); ?> >Nursery One</option>
        <option value="nursery2" <?php echo selected($nursery2, $class); ?> >Nursery Two</option>
    </select>
    <input type="button" name="class_submit" value="GO">
</form>
<form action="" method="POST">

<?php
if (ISSET($_POST['class'])) {
    $class = mysqli_real_escape_string($con, $_POST['class']);
    $student_name = mysqli_query($con, "SELECT * FROM stu_tbl WHERE `class` = '.$class.'");

    // your remaining script

    // fetch your option here

    echo '<input type="hidden" name="class" value="'.$class.'">';
}
?>

<input type="submit" name="submit" value="submit">
</form>