Correct option is C
A 'level line' is a line that is parallel to the mean spheroidal surface of the Earth. It is essentially a line that maintains a constant elevation relative to the Earth's surface, accounting for the curvature of the Earth. This line is crucial in surveying and leveling tasks to ensure accurate measurements.
Horizontal line: Refers to a line that is level with respect to gravity but not necessarily parallel to the Earth's mean surface.
Line passing through the center of cross hairs and the center of eye piece: Refers to the optical alignment of surveying instruments, not a level line.
Line passing through the objective lens and the eye-piece of a dumpy or tilting level: Describes the optical axis of the instrument, not the level line.
Therefore, the correct answer is (c) Line parallel to the mean spheroidal surface of Earth.