**Core Concept**
Hydatidiform mole, also known as a molar pregnancy, is a type of gestational trophoblastic disease. It occurs when there is an abnormal fertilization of an egg, leading to an overgrowth of trophoblastic cells that normally form the placenta. This results in a non-viable embryo and an abnormal uterine environment.

**Why the Correct Answer is Right**
The correct answer is associated with an increased level of human chorionic gonadotropin (hCG), a hormone produced by the placenta. In a normal pregnancy, hCG levels increase and peak around the 10th week of gestation. However, in a hydatidiform mole, hCG levels are often elevated and persistently high, even after the expected date of delivery. This is because the trophoblastic cells in the mole continue to produce hCG, leading to high levels in the maternal serum.

**Why Each Wrong Option is Incorrect**
**Option A:** Beta-human chorionic gonadotropin (β-hCG) is indeed elevated in a hydatidiform mole, but it's not the specific association we're looking for. Beta-hCG is a subunit of hCG.

**Option B:** Progesterone levels may be elevated in early pregnancy but are not specifically associated with hydatidiform mole.

**Option C:** FSH (Follicle-Stimulating Hormone) levels are not directly associated with hydatidiform mole.

**Option D:** While it's true that hCG is a placental hormone, the specific association we're looking for is the abnormal elevation of hCG levels in a hydatidiform mole.

**Clinical Pearl / High-Yield Fact**
A key point to remember is that a rising β-hCG level after 10 weeks of gestation is often indicative of a molar pregnancy or other gestational trophoblastic disease.

**Correct Answer:** A. Human chorionic gonadotropin (hCG).