The trick to this question is recalling the short list of tumours famous for laminated calcific spheres and then spotting the one that does not belong. Psammoma bodies appear where there is papillary growth and ongoing cell death with dystrophic calcification, building up in concentric onion-skin rings.
Run through the options. Papillary thyroid carcinoma is the prototype, with psammoma bodies sitting in the cores of its branching papillae. Serous cystadenocarcinoma of the ovary, again a papillary serous tumour, is another classic source. Meningioma, particularly the psammomatous subtype, is so associated with these bodies that the name reflects it. All three fit the papillary or serous theme.
Follicular carcinoma of the thyroid breaks the pattern. It is defined not by papillae or psammoma bodies but by invasion of the capsule and of blood vessels by an otherwise bland follicular pattern. Lacking papillary architecture, it does not form these calcified bodies, making it the correct exception.
\[\boxed{\text{Follicular carcinoma of thyroid}}\]