**Core Concept**
The population covered by a Primary Health Centre (PHC) is a fundamental concept in rural and community health, as it determines the scope and capacity of health services provided. In India, the PHC is the first referral unit that provides comprehensive primary healthcare services to rural populations. The population coverage is critical in planning and delivering healthcare services.

**Why the Correct Answer is Right**
In a hilly region, the population covered by a PHC is 20,000 due to the unique geography and accessibility challenges. The Indian government has specified this population coverage for hilly, tribal, and backward areas to ensure that the PHC can effectively reach and serve the local population. This population size allows for a more focused and personalized approach to healthcare, taking into account the specific needs and challenges of the area.

**Why Each Wrong Option is Incorrect**
**Option B:** 30,000 is the standard population coverage for a PHC in plain areas, not hilly regions. This option is incorrect because it fails to account for the unique challenges and needs of hilly areas.
**Option C:** 40,000 is an unrealistically high population coverage for a PHC in any region, let alone a hilly area. This option is incorrect because it overestimates the capacity and resources of a PHC.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that the population coverage of a PHC can vary depending on the region and the specific health needs of the population. In hilly regions, a population coverage of 20,000 is critical to ensure effective and accessible healthcare services.

**✓ Correct Answer: A. 20000**