Both major categories of shaft bearings can be mounted in which of the following ways?

Pillow block and flange mountings are indeed the correct classifications for how major categories of shaft bearings can be mounted. Pillow block bearings are typically mounted to a base or surface with bolts and provide support for a rotating shaft. They can accommodate linear movement of the shaft as well as provide stability. Flange bearings, on the other hand, usually feature a flange for ease of mounting to a surface and can provide support for both axial and radial loads.

Answering with the other options, while choices like "Four bolt and two bolt" could describe types of mounting configurations, they don't specifically relate to the categories of bearings. "Single assembly and split assembly" references the configuration of bearings rather than their mounting styles. Thus, the pillow block and flange categories accurately reflect the specific mounting methods associated with shaft bearings.