Step 1: Vitamin K acts as a cofactor for the enzyme that carboxylates glutamate residues on certain clotting factors. This gamma-carboxylation lets these factors bind calcium and attach to phospholipid surfaces, which they need to work.
Step 2: The vitamin K dependent clotting factors are II, VII, IX and X (a useful memory aid is the numbers 1972, that is factors 10, 9, 7, 2). Protein C and protein S, two anticoagulants, are also vitamin K dependent.
Step 3: Now check the options. Option B lists IX and X, both of which are on the list, so it is correct.
Step 4: The other options each contain a factor that is not vitamin K dependent. Option A pairs II (dependent) with III, which is tissue factor and is not vitamin K dependent. Option C has III and V, neither of which is vitamin K dependent. Option D has VIII and XII, neither of which is vitamin K dependent.
Conclusion: Factors IX and X are vitamin K dependent. Answer is option B.