Matching the clinical signs with their associated diseases:
(A) Murphy's sign: This sign is elicited during palpation of the right upper quadrant of the abdomen. Pain on inspiration when the examiner's fingers are under the right costal margin suggests inflammation of the gallbladder, commonly seen in Acute Cholecystitis (II).
(B) Rovsing's sign: This sign is elicited by deep palpation in the left lower quadrant of the abdomen, which causes pain in the right lower quadrant. It is indicative of peritoneal irritation in Acute Appendicitis (III).
(C) Iliopsoas sign: This sign is elicited by extending the thigh of a patient lying on their side against resistance or by passively extending the thigh of a supine patient. Pain indicates irritation of the iliopsoas muscle, which can occur in conditions such as Iliopsoas Abscess or Perinephric Abscess (I) where the inflamed structures are adjacent to the muscle.
(D) Grey Turner's and Cullen's signs: These are signs of retroperitoneal haemorrhage. Grey Turner's sign refers to ecchymosis (bruising) of the flanks, while Cullen's sign refers to ecchymosis around the umbilicus. These can be seen in conditions like Haemorrhagic pancreatitis, aortic rupture, and ruptured ectopic pregnancy (IV).
Therefore, the correct matching is (A)-(II), (B)-(III), (C)-(I), (D)-(IV).