precarious position vs. peculiar position

[Lost_Soul]

English Language Proficiency Tests, Advanced Level

ESL/EFL Test #88 "Verbal Advantage", question 9

He found himself at the edge of the cliff in a ......... position because one wrong step and he would fall into the sea.

(a) precipitate
(b) peculiar
(c) pertinent
(d) precarious

English Language Proficiency Tests, Advanced Level

ESL/EFL Test #88 "Verbal Advantage", answer 9

He found himself at the edge of the cliff in a precarious position because one wrong step and he would fall into the sea.

Correct answer: (d) precarious

Your answer was: incorrect
He found himself at the edge of the cliff in a peculiar position because one wrong step and he would fall into the sea.
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technically speaking, is "peculiar" possible here?

[Mister Micawber]

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It is not a question of technology; 'peculiar' is incongruous with the intimation of 'one wrong step and he would fall into the sea'.
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Native English teacher at Mister Micawber's