**Core Concept**
The Neonatal Mortality Rate (NMR) is a crucial indicator of infant health, defined as the number of deaths within the first 28 days of life per 1,000 live births.

**Why the Correct Answer is Right**
To calculate NMR, we need to consider the total number of live births (excluding stillbirths) and the number of deaths within the first 28 days of life. The formula for NMR is: (Number of deaths within 0-27 days of life / Total live births) * 1000. In this scenario, there are 4050 total births, with 50 stillbirths, leaving us with 4000 live births. The number of deaths within the first 28 days is 50 (within the first 7 days) + 150 (within 8-28 days) = 200 deaths.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not account for the stillbirths in the calculation.

**Option B:** This option is incorrect because it incorrectly adds the number of stillbirths to the total number of live births.

**Option C:** This option is incorrect because it uses the total number of births (including stillbirths) instead of live births.

**Option D:** This option is incorrect because it uses the number of deaths within the first 7 days only, ignoring the deaths within 8-28 days.

**Clinical Pearl / High-Yield Fact**
Remember, when calculating NMR, it's essential to exclude stillbirths from the total number of births and consider deaths within the first 28 days of life.

**Correct Answer:** 50.