The sentence describes a scientific observation: layers in rock that stood out or were not typical for that time. So, the blank must be filled by an adjective that describes the unexpected or rare nature of the rock layers.
(a) dancing (verb/adjective - present participle): Grammatically inappropriate - Although participles can act as adjectives, "dancing" is unrelated to geological layers. Contextually incorrect - Rock layers do not "dance"; the word makes no logical sense here.
(b) idea (noun): Grammatically invalid - a noun cannot directly modify another noun ("layers") without a linking verb or preposition. Contextually irrelevant - "idea" refers to a concept, not a physical quality of geological formations.
(c) quickly (adverb): Grammatically invalid - adverbs modify verbs, not nouns. It cannot describe "layers." Contextually irrelevant - speed is not a property of physical rock layers.
(d) jump (verb/noun): Grammatically invalid - both as a noun and a verb, "jump" cannot modify "layers." Contextually meaningless - there is no jumping action associated with sedimentary deposition.
(e) unusual (adjective): Grammatically appropriate - modifies the noun "layers." Contextually accurate - fits the meaning perfectly, describing rock layers that were anomalous or unexpected based on past geological patterns.
Only (e) "unusual" is both grammatically correct and contextually meaningful in describing the layers of rock observed.
Hence, option (e) is the correct answer.