how to remove the default title of Categories widget

There is a filter you can use to do this. (Kruti has even found it, but instead of using it, he modified core files…)

$title = apply_filters('widget_title', empty( $instance['title'] ) ? __( 'Categories' ) : $instance['title'], $instance, $this->id_base);

So what you really need to do, is to add this to your functions.php:

function my_repair_categories_empty_title($title, $instance, $base) {
    if ( $base == 'categories' ) {
        if ( trim($instance['title']) == '' )
            return '';
    }
    return $title;
}
add_filter('widget_title', 'my_repair_categories_empty_title', 10, 3);