Step 1: Muscarinic antagonists (e.g. atropine) block the parasympathetic (cholinergic) effects mediated by muscarinic receptors.
Step 2: Blocking muscarinic receptors on gastric parietal cells reduces acid and fluid secretion, so option A (decreases gastric secretion) is a true action.
Step 3: By removing vagal (parasympathetic) tone at the AV node, antimuscarinics speed up AV conduction and increase heart rate. Wait, the expected antimuscarinic effect on the AV node is to FACILITATE conduction; however the key exception in this question is the iris. Atropine blocks secretions, so option C (decreases tracheobronchial secretions) is a true antisecretory action.
Step 4: Pupillary effect: mydriasis (pupil dilation) produced by atropine is due to PARALYSIS of the circular (sphincter) muscle of the iris, which is muscarinically innervated. The radial (dilator) muscle is sympathetically innervated and is NOT contracted by an antimuscarinic. So option D, contraction of the radial muscles of the iris, is NOT an action of a muscarinic antagonist.
Step 5: The exception is option D, which is the correct answer. Antimuscarinics dilate the pupil by relaxing the sphincter, not by contracting the dilator.