Statement (A): Back Bearing of a line is equal to Fore Bearing \( \pm 180^\circ \).
This statement is correct. In surveying, the back bearing is the reverse direction of the fore bearing. The relationship is given by:
\[
\text{Back Bearing} = \text{Fore Bearing} \pm 180^\circ
\]
If the fore bearing is between 0° and 180°, add 180° to find the back bearing. If the fore bearing is between 180° and 360°, subtract 180° to find the back bearing.
Statement (B): If the whole circle bearing of a line is 270°, its reduced bearing is 90° NW.
This statement is also correct. The whole circle bearing of 270° corresponds to the reduced bearing of 90° NW. Reduced bearings are measured from the North or South, with angles less than 90° from the reference direction, and in this case, the bearing is 90° to the west from the North, which is 90° NW.
Statement (C): The boundary of water of a calm water pond will represent contour line.
This statement is correct. The boundary of water in a calm water pond, which remains at a constant level, forms a horizontal surface. In contour mapping, a contour line represents a line of constant elevation. Therefore, the boundary of water in a pond corresponds to a contour line at the water level.
Statement (D): In the case of fixed hair stadia tachometry, the staff intercept will be larger, when the staff is held nearer to the observation point.
This statement is incorrect. In stadia tachometry, the staff intercept is inversely proportional to the distance from the instrument. If the staff is held nearer to the observation point, the staff intercept will be smaller, not larger.
Final Answer: (A), (B), (C)