Which one of the following depresses brain activity and produces feelings of calmness, relaxation and drowsiness -

Sedatives and tranquillisers depress the activity of the brain and produce feelings of calmness, relaxation and drowsiness.
Valium (diazepam) is a benzodiazepine tranquilliser, used to treat anxiety and sleeplessness. So it produces these effects.
Morphine is an opiate narcotic, used as a powerful painkiller.
Hashish is a cannabinoid that alters thoughts, perceptions and feelings (hallucinogenic effect).
Amphetamines are stimulants that increase alertness and activity.
So the drug that depresses brain activity and produces calmness, relaxation and drowsiness is Valium.