How to pass argument that is not input field in laravel blade ?

I can pass input field value to controller by using format that shown below

       <form method="GET" action="{{Request::fullUrl()}}">

However, how can I pass the value that is not input field such as bootstrap dropdown value ?

And anyone know how to set request argument using laravel 5 ? for example, Request::get('search') gives me baseurl/search=

via Chebli Mohamed