$P$ is the brother of $Q$, who is the sister of $R$. $S$ is the brother of $T$ and $T$ is the mother of $Q$. How is $S$ related to $Q$?

Let's break down the relations given in the question step-by-step:
1. $P$ is the brother of $Q$ and $Q$ is the sister of $R$. This means $P,Q,R$ are siblings.
2. $T$ is the mother of $Q$. Since they are siblings, $T$ is the mother of $P,Q,$ and $R$.
3. $S$ is the brother of $T$.

Since $S$ is the brother of $Q$ 's mother ($T$), $S$ is the maternal uncle of $Q$. Thus, the broad relation option matches Uncle.