$file = "endereço/meu_arquivo.pdf";

$mime_types = array(
    //mime do pdf
    'pdf' => 'application/pdf',

    //mimes do Word
    'doc' => 'application/msword',
    'docm' => 'application/vnd.ms-word.document.macroenabled.12',
    'docx' => 'application/vnd.openxmlformats-officedocument.wordprocessingml.document',
    'dot' => 'application/msword',
    'dotm' => 'application/vnd.ms-word.template.macroenabled.12',
    'dotx' => 'application/vnd.openxmlformats-officedocument.wordprocessingml.template',

    //Mimes do excel
    'xl' => 'application/excel',
    'xlam' => 'application/vnd.ms-excel.addin.macroenabled.12',
    'xlf' => 'application/x-xliff+xml',
    'xlsb' => 'application/vnd.ms-excel.sheet.binary.macroenabled.12',
    'xlsm' => 'application/vnd.ms-excel.sheet.macroenabled.12',
    'xlsx' => 'application/vnd.openxmlformats-officedocument.spreadsheetml.sheet',
    'xltm' => 'application/vnd.ms-excel.template.macroenabled.12',
    'xltx' => 'application/vnd.openxmlformats-officedocument.spreadsheetml.template',
);

//Pega a extensão do arquivo
$ext = pathinfo($file, PATHINFO_EXTENSION);

//usa a extensão como chave para procurar o mime correto e envia ao navegador
header('Content-type: ' . $mime_types[$ext]);