Which of the following errors cannot be eliminated by taking both face observations ?

Solution (By Examveda Team)

In theodolite surveying, taking both face left and face right observations is a common technique to eliminate symmetrical instrumental errors.

These errors are usually equal in magnitude but opposite in sign when the instrument is reversed, so averaging both readings cancels them out.

Option A: Error due to the horizontal axis not being perpendicular to the vertical axis
This error is symmetrical and can be eliminated by taking both face observations.

Option B: Index error due to imperfect adjustment of the vertical circle vernier
This is also a symmetrical error and can be eliminated by taking face left and face right readings.

Option C: Error due to non-parallelism of the axis of telescope level and the line of collimation
This is an asymmetrical and inherent instrument error. It affects the sighting line itself and cannot be eliminated by reversing the face of the instrument.

Option D: None of the above
This is incorrect because one of the options (Option C) is indeed a valid exception.

Therefore, the correct answer is: error due to non-parallelism of the axis of telescope level and line of collimation (Option C).