Particles in a solid exhibit vibrational motion.
In a solid, the particles are closely packed together and held in a fixed position by strong intermolecular forces. However, the particles are not completely motionless. They can vibrate around their fixed positions due to thermal energy.
The amount of energy available for this vibrational motion is determined by the temperature of the solid. As the temperature increases, the particles vibrate more vigorously. However, the particles do not move from their positions in the solid, and so they do not exhibit translational motion.
Therefore, the correct answer is that particles in a solid exhibit vibrational motion. The other options (vibrational and translational motion, vibrational and random motion, and random and translational motion) are not correct because they describe the motion of particles in liquids or gases, where the particles are free to move and exhibit translational or random motion in addition to vibrational motion.