In Arabic morphology (علم الصرف), the word مكتبة (library/bookshop) is derived from the root ك-ت-ب (related to writing). To find its morphological pattern (الوزن الصرفي), we map the root letters onto the standard template فعل: ك = ف, ت = ع, ب = ل. The prefix م indicates a noun of place (اسم المكان), and the suffix ة (taa marbuta) marks it as feminine. The resulting pattern is therefore مَفْعَلَة.
This pattern مَفْعَلَة is commonly used to form nouns of place in Arabic. Other examples include: مَدْرَسَة (school, from د-ر-س, to study), مَطْبَعَة (printing press, from ط-ب-ع, to print), and مَكْتَبَة itself (a place of writing/books). The other options are incorrect: فَعْلَة is a simple noun pattern without the م prefix; مَفْعَل is a noun-of-place pattern but without the feminine ending; and فاعِل is the active participle pattern (e.g., كاتِب, writer).
Exam tip: When determining the وزن صرفي, always extract the root letters first, then identify any added letters (prefixes, infixes, suffixes) and match them to a known pattern.