**Solution:**

To solve this question, we need to find the correct time when the watch is showing the correct time. Let's analyze the given information step by step.

**Step 1: Determine the watch's gain per day**
- The watch gains uniformly, so we can determine its daily gain by finding the difference between the two given times.
- The watch is 2 minutes slow at noon on Monday and 4 minutes 48 seconds fast at 2 p.m. on the following Monday.
- The time difference between these two is 6 days and 2 hours (or 50 hours).
- The watch gains (4 minutes 48 seconds - 2 minutes) in 50 hours.
- To find the daily gain, we divide the overall gain by the number of days:
- Daily gain = (4 minutes 48 seconds - 2 minutes) / 6 days
- Daily gain = 2 minutes 48 seconds / 6 days
- Daily gain = 28 seconds / day

**Step 2: Determine when the watch shows the correct time**
Now, we need to determine the correct time when the watch is neither fast nor slow.

To do this, we need to consider that the watch gains 28 seconds per day. We also know that the watch is 2 minutes slow at noon on Monday. So, we need to calculate the time it takes for the watch to gain 2 minutes (120 seconds).

- Time taken for the watch to gain 120 seconds = (120 seconds) / (28 seconds/day)
- Time taken = 4.2857 days

**Step 3: Determine the correct day and time**
We know that the watch is 2 minutes slow at noon on Monday. To find when the watch shows the correct time, we need to add the time taken from step 2 to Monday noon.

- Correct day = Monday + 4.2857 days
- Correct day = Friday

So, the correct time is on Friday. Now, we need to determine the correct time on Friday.

- Correct time = Noon + 4.2857 days
- Correct time = 1 p.m.

Therefore, the correct time is 1 p.m. on Friday.

**Answer:**
The watch shows the correct time at 1 p.m. on Friday, which corresponds to option D.