Explanation:
A theodolite is a precise instrument used in surveying and engineering to measure horizontal and vertical angles. It consists of a telescope mounted on a base with a horizontal and vertical circle.

There are several adjustments that can be made to a theodolite to ensure its accuracy and reliability. These adjustments can be categorized into two types: temporary adjustments and permanent adjustments.

Temporary adjustments:
Temporary adjustments are made each time the theodolite is set up and used in the field. These adjustments include leveling the instrument, centering the instrument over a point, and setting the vertical and horizontal circles to zero.

Permanent adjustments:
Permanent adjustments are made to the theodolite to correct any errors or misalignments that may occur over time. These adjustments are typically made during the manufacturing process or during regular maintenance and calibration of the instrument. The permanent adjustments include:

1. Elimination of parallax: Parallax occurs when the image seen through the telescope appears to move relative to the reticle or crosshairs. This can cause errors in angle measurements. The elimination of parallax adjustment ensures that the image seen through the telescope is focused and aligned with the reticle, eliminating any parallax.

2. Adjustment of the vertical circle index: The vertical circle index is used to measure vertical angles. This adjustment ensures that the vertical circle index is properly aligned with the reference mark on the instrument, allowing for accurate vertical angle measurements.

3. Adjustment of the telescope: The telescope is mounted on the theodolite and is used to sight the target or point of interest. This adjustment ensures that the telescope is properly aligned and focused, allowing for accurate sighting of the target.

4. Adjustment of the horizontal plate level: The horizontal plate level is used to level the theodolite. This adjustment ensures that the theodolite is level and stable, allowing for accurate horizontal angle measurements.

Correct answer:
The correct answer is option A, elimination of parallax. This is because the elimination of parallax adjustment is a permanent adjustment made to the theodolite to ensure accurate angle measurements. The other options, adjustment of the vertical circle index, adjustment of the telescope, and adjustment of the horizontal plate level, are all permanent adjustments that are necessary for the proper functioning and accuracy of the theodolite.