The correct answer is "Ragini plays the guitar melodiously."

Step-by-step Explanation:

1. Identifying the Function of the Modifier:
In the given sentence structure, "Ragini" is the subject, "plays" is the main action verb, and "the guitar" is the direct object. The word at the end of the sentence is meant to describe how Ragini plays the guitar (modifying the verb "plays").

2. Using the Correct Part of Speech:
Words that modify verbs, adjectives, or other adverbs are called adverbs. The word "melodiously" is an adverb (formed by adding the suffix -ly to the adjective melodious). Therefore, it correctly modifies the verb "plays" to show the manner in which the action is performed.

3. Analysis of Incorrect Options:
• "Ragini plays the guitar melodious." – Incorrect because "melodious" is an adjective, and adjectives modify nouns, not verbs.
• "Ragini plays the guitar with a melody." – Incorrect/awkward because "with a melody" is redundant and unnatural for describing the manner of playing.
• "Ragini plays the guitar with melodiousness." – Incorrect/awkward because using the abstract noun "melodiousness" creates a wordy and non-standard sentence construction when a simple adverb ("melodiously") exists.

Thus, "Ragini plays the guitar melodiously." is the only grammatically correct and naturally phrased sentence.