The greatest difference in the concentration of respiratory gases is found in which of the following pairs of mammalian blood vessels?

The pulmonary vein and the jugular vein.

Explanation:

The greatest difference between the pulmonary vein and the jugular vein is that pulmonary vein takes oxygenated blood from both lungs towards the left atrium of heart while jugular vein takes the deoxygenated blood from head back towards right atrium of heart through superior vena cava.

So, the main difference is oxygenated and deoxygenated blood in the above mentioned veins.