Mean, display list of categories and archieve in Drop Down menu style.

Code For category:

<div id="cats"><?php wp_dropdown_categories('show_option_none=Select Category'); ?>

<script type="text/javascript"><!--
var dropdown = document.getElementById("cat");
function onCatChange() {
if ( dropdown.options[dropdown.selectedIndex].value > 0 ) {
location.href = "<?php echo get_option('home');
?>/?cat="+dropdown.options[dropdown.selectedIndex].value;
}
}
dropdown.onchange = onCatChange;
--></script>

 and code for Archieve:

<div id="archive"><select name="archive-dropdown" onchange="document.location.href=this.options[this.selectedIndex].value;">
<option value=""><?php echo esc_attr( __( 'select Month' ) ); ?></option>
<?php wp_get_archives( array( 'type' => 'monthly', 'format' => 'option', 'show_post_count' => 1 ) ); ?>
</select></div>

Combine both codes in Table, like this:

<table>
<tr>
<th>
News by Month
<div id="archive"><select name="archive-dropdown" onchange="document.location.href=this.options[this.selectedIndex].value;">
<option value=""><?php echo esc_attr( __( 'Select Month' ) ); ?></option>
<?php wp_get_archives( array( 'type' => 'monthly', 'format' => 'option', 'show_post_count' => 1 ) ); ?>
</select></div>

</th>
<th>
News by Topic:
<div id="cats"><?php wp_dropdown_categories('show_option_none=Select Category'); ?>

<script type="text/javascript"><!--
var dropdown = document.getElementById("cat");
function onCatChange() {
if ( dropdown.options[dropdown.selectedIndex].value > 0 ) {
location.href = "<?php echo get_option('home');
?>/?cat="+dropdown.options[dropdown.selectedIndex].value;
}
}
dropdown.onchange = onCatChange;
--></script>
</div>
</th>
</tr>
</table>