There are times when you need to exclude posts belonging to certain categories in your custom pages or archives, after scouring the internet, i take no credit for these, but this can simply be achieved by using the following code snippets:

Exclude a category from custom pages or archive pages in wordpress:

The following applies to all date archive pages and hides posts which are listed in category 6.
(place this code into your theme’s functions.php file)

function exclude_stuff($query) {
if ( $query->is_date) {
		$query->set('cat', '-6');
}
return $query;
}
add_filter('pre_get_posts', 'exclude_stuff');

Exclude a category from the Archives Dropdown and updates count (in brackets)

The example below excludes posts in category ID 6:

add_filter( 'getarchives_where', 'customarchives_where' );
add_filter( 'getarchives_join', 'customarchives_join' );

function customarchives_join( $x ) {
	global $wpdb;
	return $x . " INNER JOIN $wpdb->term_relationships ON ($wpdb->posts.ID = $wpdb->term_relationships.object_id) INNER JOIN $wpdb->term_taxonomy ON ($wpdb->term_relationships.term_taxonomy_id = $wpdb->term_taxonomy.term_taxonomy_id)";
}

function customarchives_where( $x ) {
	global $wpdb;
	$exclude = '6'; // category id to exclude
	return $x . " AND $wpdb->term_taxonomy.taxonomy = 'category' AND $wpdb->term_taxonomy.term_id NOT IN ($exclude)";
}