The correct answer is: A. error due to eccentricity of verniers.
The method of repetition of horizontal angle measurement is a technique used to reduce the effects of random errors in angle measurement. The basic idea is to measure the angle multiple times and then average the results. This reduces the effect of any individual error, as long as the errors are random.
However, there are some errors that cannot be eliminated by this method. One such error is the error due to eccentricity of verniers. This error occurs when the vernier scale is not perfectly aligned with the main scale. This can cause the vernier reading to be off by a small amount, which will be cumulative over multiple measurements.
The other options are all errors that can be reduced or eliminated by the method of repetition of horizontal angle measurement. Error due to displacement of station signals can be reduced by using a stable tripod and by taking care to set up the signals in the same position each time. Error due to wrong adjustment of line of collimation and trunnion axis can be eliminated by carefully adjusting the instrument before taking measurements. Error due to inaccurate graduation can be reduced by using a high-quality instrument and by taking care to read the vernier scale accurately.
In conclusion, the error due to eccentricity of verniers is the only error that cannot be eliminated by the method of repetition of horizontal angle measurement.