Explanation:
The correct answer is C: rotatory and nodding movements.

The joint between the atlas (C1) and the axis (C2) vertebrae allows for both:
- Rotatory movement: This allows the head to turn from side to side, as seen when shaking the head.
- Nodding movement: This allows for up-and-down motion, as seen when nodding the head.

These movements are possible because of the unique structure of the atlas and axis, where the atlas supports the skull and pivots around the odontoid process (also known as the dens) of the axis. This is a specialized type of joint that provides flexibility for these two kinds of movement.

Here’s why the other options are incorrect:
- A: rotatory movement only: This is not entirely correct because the joint allows both rotatory and nodding movements.
- B: up and down or nodding movements only: This excludes the rotational movement, which is also allowed.
- D: no movement at all: This is incorrect because the joint allows for significant movement.
- E: slight movement: The joint allows for more than just slight movement; it enables both nodding and rotation.

Thus, C: rotatory and nodding movements is the correct answer.