**Core Concept**
Warfarin is a vitamin K antagonist that inhibits the production of various clotting factors in the liver, leading to a decrease in blood coagulability. The clotting factors affected by warfarin are part of the extrinsic and common coagulation pathways.

**Why the Correct Answer is Right**
Warfarin exerts its effect by inhibiting the gamma-carboxylation of glutamate residues on vitamin K-dependent clotting factors, making them inactive. The first clotting factor to fall in level after warfarin administration is Factor VII, which is part of the extrinsic coagulation pathway. This is because Factor VII has the shortest half-life among the vitamin K-dependent clotting factors, making it the first to be affected by warfarin. The decrease in Factor VII level is detectable within 24-48 hours after warfarin initiation.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect as Factor X is not the first clotting factor to fall in level after warfarin administration. While Factor X is also a vitamin K-dependent clotting factor, its half-life is longer than that of Factor VII, making it less sensitive to warfarin.
* **Option B:** This option is incorrect as Factor II (prothrombin) is not the first clotting factor to fall in level after warfarin administration. Like Factor X, the half-life of Factor II is longer than that of Factor VII, making it less sensitive to warfarin.
* **Option D:** This option is incorrect as Factor IX is not the first clotting factor to fall in level after warfarin administration. The half-life of Factor IX is longer than that of Factor VII, making it less sensitive to warfarin.

**Clinical Pearl / High-Yield Fact**
The effect of warfarin on clotting factor levels can be monitored using the prothrombin time (PT) and international normalized ratio (INR) tests. It's essential to note that the INR is a more sensitive measure of warfarin's effect on clotting factor levels, especially in the early stages of treatment.

**Correct Answer: C. Factor VII. Factor VII is the first clotting factor to fall in level after warfarin administration.**