The correct answer is option 'A' (i) and (ii) - oscillatory motion and vibratory motion.

Oscillatory Motion:
When a guitar string is plucked, it vibrates back and forth. This back and forth motion is called oscillatory motion. The string moves away from its original position and then returns back to it. This motion continues until the energy of the pluck is fully dissipated. The oscillatory motion of the guitar string is responsible for producing sound waves, which we hear as musical notes.

Vibratory Motion:
Vibratory motion is similar to oscillatory motion, but it refers to the rapid back and forth motion of an object or particle. In the case of a guitar string, when it is plucked, it undergoes vibratory motion as it rapidly vibrates back and forth. This motion is responsible for creating the sound waves that produce musical notes.

Explanation:
The motion of guitar strings can be described as both oscillatory and vibratory. When a guitar string is plucked, it moves away from its equilibrium position and then comes back to it. This back and forth motion is oscillatory in nature. The string vibrates rapidly, creating sound waves that produce musical notes. This rapid motion is considered as vibratory motion.

The other options (iii) random motion and (iv) rotational motion are not applicable to the motion of guitar strings.

Random Motion:
Random motion refers to unpredictable and irregular motion. The motion of guitar strings is not random because it follows a specific pattern of oscillation and vibration.

Rotational Motion:
Rotational motion refers to the motion of objects around an axis or center of rotation. The guitar string does not rotate around an axis. Instead, it moves back and forth in a linear motion.

In conclusion, the motion of guitar strings can be described as both oscillatory and vibratory, making option 'A' (i) and (ii) the correct answer.