Show only “Pages” – not posts – on search page

Setting the post type at pre_get_posts can solve this. You can set it like below-

function the_dramatist_search_only_page($query) {

    if ($query->is_search && !is_admin() ) {
        $query->set('post_type',array('page'));
    }

    return $query;
}

add_filter('pre_get_posts','the_dramatist_search_only_page');

Hope it helps.