Meaning & usage
べくもない expresses that there is no possible way to do something, often that a fact or feeling is beyond knowing, guessing, imagining or recalling. It attaches to the dictionary form of a verb, as in 知るべくもない or 想像するべくもない, and becomes べくもなかった for the past. It is a formal, written style and is not used for ordinary controllable actions, where forms like ようもない are natural.
Example sentences 3
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彼の気持ちは察するべくもない。
There is no way to guess how he feels.
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あの日のことは思い出すべくもない。
There is no way to recall what happened that day.
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彼の成功は疑うべくもない事実だ。
His success is a fact beyond doubt.
In past JLPT papers
This came up in 1 past exam question.