Where the word "Near" is used as preposition ?

In the sentence "My school is near the mosque," the word "near" is used as a preposition. It shows the spatial relationship (location/proximity) between the noun "school" and the noun phrase "the mosque". Prepositions are always followed by a noun or pronoun (known as the object of the preposition). 

Why other options are incorrect

খ) Draw near and listen: Here, "near" is used as an adverb, modifying the verb "Draw" by indicating where to draw (draw close/nearby). It does not take an object.

গ) She is a near relation: In this sentence, "near" is an adjective that describes the noun "relation" (meaning close or intimate relation).

ঘ) Death nears with the passage of time: In this instance, "nears" is a verb, meaning "approaches" or "gets close".