The disease transmitted only by inheritance among the options is (c) Haemophilia. It is a genetic disorder characterized by a deficiency in clotting factors, primarily factor VIII (hemophilia A) or factor IX (hemophilia B). Haemophilia is inherited through a recessive X-linked pattern, meaning it primarily affects males who inherit the defective gene on their X chromosome from their carrier mother. While myocardial infarction (a), diabetes mellitus (b), and cancer (d) can have genetic components, they can also result from various environmental and lifestyle factors, not solely inheritance.