のに(purpose) — In order to / For the purpose of

• この辞書は日本語を学ぶのに役立ちます。

  Kono jisho wa nihongo wo manabu no ni yakudachimasu.

  This dictionary is useful for learning Japanese.

  学ぶのに (for the purpose of learning) + 役立つ

• 料理をするのに時間がかかる。

  Ryouri wo suru no ni jikan ga kakaru.

  Cooking takes time.

  するのに時間がかかる = for the act of cooking, time is needed

• この鍵はドアを開けるのに使います。

  Kono kagi wa doa wo akeru no ni tsukaimasu.

  This key is used to open the door.

  開けるのに使う = use it for the purpose of opening

• ・のに (purpose) vs ために (purpose): ために suits volitional verbs and personal goals; のに suits function/use/necessity, especially with inanimate subjects.
• ・Nuance: 勉強するのに役立つ (useful for studying) vs 勉強するために毎日頑張る (work hard in order to study).

Commonly confused with

The JLPT rarely asks whether you recognise a pattern — it asks which of several similar patterns fits. These are the ones のに is tested against.

• ために — Purpose / Benefit (in order to / for the sake of)
• ように — Goal / Hope (so that ...)