Which of these cattle diseases is genetically linked with the age of 7-9 years?

Lymphosarcoma is the correct answer because it is a type of cancer that is indeed known to be affected by the animal's age, particularly in cattle. This disease often manifests in cows that are around 7 to 9 years old. Lymphosarcoma is closely associated with the lymphatic system and can lead to significant health issues, including tumors in various organs.

The age correlation is significant; while cattle generally can develop various diseases throughout their lives, lymphosarcoma has a particularly high incidence in the specified age range due to genetic predispositions and other risk factors that emerge as the animals mature.

In contrast, the other diseases mentioned have different characteristics and age implications. Brucellosis primarily impacts younger cattle and does not directly correlate with a specific age range in the same way. Johne's disease, a chronic intestinal infection, often shows symptoms in younger animals, typically before they reach the age range mentioned. Foot and mouth disease is an infectious viral disease that can affect animals of any age but does not have a genetic predisposition linked to a specific age. Thus, the distinctive association between lymphosarcoma and the age of 7-9 years makes it the most appropriate choice in this context.