Which word correctly completes the sentence below? These French history lessons have a rather __________ effect on me; I keep nodding off and sleeping through major periods.

The correct answer is sedate.
In order to modify a noun effect found in this sentence, you need to use an adjective, and the word sedate is the only adjective among the possible options. Sedately is an adverb and it could modify a verb, sedateness and sedation are both nouns and therefore cannot be used here.