Part CCSIR NET December 2024a-connected-domain-forces-a-constant-map

A connected domain forces a constant map

Which of the following statements are true?

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

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

50 are analysed free — try those first.

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