門の所にだれかが立っている。

建つ (たつ)
Meaning: to be built
Used for buildings or structures, such as houses or bridges.
•家が建つ A house is built.

立つ (たつ)
Meaning: to stand upright
Used for people or things that stand on their own.
•人が立つ A person is standing.

解答例：問題が生じる

生じる（しょうじる） is a more formal and advanced alternative to 起きる（おきる）.

examples:
問題が生じる / a problem arises.
誤解が生じる / misunderstandings arises
混乱が生じる / confusion arises

B) 帽子をかぶる is more natural.

The verb changes depending on where and how the item is worn.

Upper body (e.g., T-shirts, coats) → 着る（きる）
Lower body (e.g., pants, shoes) → 履く（はく）
Glasses → かける
Jewelry → つける

The answer is A) 物価が上がる.

上がる（あがる） is an intransitive verb, so it is used as:
👉 something が上がる
上げる（あげる） is a transitive verb, so it is used as:
👉 (someone が) something を上げる

Example:
・物価が上がる
・政府が税金を上げる