A connected domain forces a constant map

1. A.Let $x, y \in \mathbb{R}$ with x < y. Then there exists $r \in \mathbb{Q}$ such that x < (2^2024/e)r < y.✓ Correct
2. B.Let $(a_{n})_{n}\ge_{2}$ be a sequence of positive real numbers. If there exists a positive real number L such that $\lim \sup(n\to\infty) a_{n}/\log n = L$, then $\lim \sup(n\to\infty) a_{n} < \infty$.
3. C.The set of all finite subsets of $\mathbb{Q}$ is countably infinite.✓ Correct
4. D.The set of continuous functions from $\mathbb{R}$ to the set {0, 1} is infinite.

The trap it tests

There is a canonical object that settles this. Recognising it is the whole question.