Concept:
Barbiturates and Benzodiazepines are CNS depressants. They are commonly used as sedatives and sleep-inducing drugs.
Step 1: Examine Statement I.
Statement I says:
\[
\text{Barbiturates cause sleeplessness}
\]
But Barbiturates are sedative-hypnotic drugs.
They induce sleep and reduce anxiety.
Therefore,
\[
\boxed{\text{Statement I is False}}
\]
Step 2: Examine Statement II.
Benzodiazepines are widely used as
\[
\text{sleeping pills}
\]
and anti-anxiety drugs.
Therefore,
\[
\boxed{\text{Statement II is True}}
\]
Step 3: Select the correct option.
Thus,
\[
\text{I = False,\quad II = True}
\]
Hence,
\[
\boxed{\text{Option (D)}}
\]
is correct.