**Core Concept**
Neonatal mortality rate (NMR) is a crucial public health indicator that measures the number of deaths occurring in the first 28 days of life per 1,000 live births in a given year. It is an essential tool for assessing the quality of healthcare services for newborns and identifying areas for improvement.

**Why the Correct Answer is Right**
To calculate the NMR, we need to first determine the number of live births, which is 4050 - 50 (stillbirths) = 4000. Next, we need to identify the number of deaths occurring in the first 28 days, which is 50 (first 7 days) + 150 (first 28 days) = 200. The NMR is then calculated as (200 / 4000) x 1000 = 50.

**Why Each Wrong Option is Incorrect**
**Option A:** This option would require a completely different calculation, using the number of deaths in the first 7 days as the numerator, which is incorrect.
**Option B:** This option would also require a different calculation, using the total number of deaths (200) as the numerator, which is incorrect because it includes deaths after 28 days.
**Option C:** This option would use the total number of deaths (200) as the numerator, which is incorrect because it includes deaths after 28 days.
**Option D:** This option would use the total number of births (4050) as the denominator, which is incorrect because it includes stillbirths.

**Clinical Pearl / High-Yield Fact**
When calculating NMR, it's essential to exclude stillbirths and only consider live births. Additionally, the NMR is often used in conjunction with other indicators, such as infant mortality rate (IMR), to assess the overall quality of healthcare services for newborns.

**Correct Answer: A. 50.