The sentence requires you to figure out the effect that “tranquilizers usually have,” and this is provided by the clue in the later part of the sentence, when you read that the “abuse of these drugs results in a failure to induce the much-desired sleep.” You can infer that the usual effect of tranquilizers is to produce sleep. Soporific, which means sleep-inducing, is the correct answer choice. While sedulous might remind you of “sedative,” it actually means hard-working.