The correct answer to the question, "Which of the following is a necessary condition for plane table surveying?" is:

The plane table must be levelled and properly oriented at each station.

Let's go through the options to understand the reasoning:

1. The plane table must be levelled and properly oriented at each station:

   Plane table surveying is a graphical method of surveying in which field observations and plotting are performed simultaneously. For accurate results in plane table surveying, it is crucial that the plane table is level and properly oriented at each station. This ensures that the angles and distances measured are accurate, which is essential for plotting the survey correctly.

2. Only a single station is required for the entire survey:

   This statement is incorrect. Plane table surveying requires multiple stations to cover the area being surveyed. More stations allow for better accuracy and completion of the survey.

3. Contours must be measured and plotted before starting the survey:

   Contours are typically determined during the surveying process, not before. Plane table surveying deals primarily with the direct plotting of the survey points on paper, not the pre-measurement and plotting of contours.

4. All the stations must be established on a slope of the terrain:

   This statement is incorrect and impractical. Stations are chosen based on their utility for covering the survey area and obtaining necessary data, not specifically based on terrain slope. Typically, locations are chosen for stability and line of sight to other stations.

In conclusion, the key requirement for successful plane table surveying is ensuring that the table is levelled and oriented properly at each station to achieve accurate and reliable results.