Arranging different oxygen-containing organic compounds by decreasing acidity
And this is the type of question for which Professor Mayr made us chemistry students rote memorise typical $\mathrm{p}K_\mathrm{a}$ values. Here are some.

\begin{array}{lc}\hline
\text{compound type} &amp; \text{typical }\mathrm{p}K_\mathrm{a}\\ \hline
\text{alcohol} &amp; \approx 15 \\
\text{ketone} &amp; \approx 20\\
\text{carboxylic acid} &amp; \approx 5\phantom{0}\\
\text{secondary }\ce{C-H} &amp; \approx 45\\ \hline\end{array}

Therefore, the order is $\mathrm{Q &gt; P &gt; R &gt; S}$