The only set which are connected in $\mathbb{R} $ are intervals
Solution: Given that $X \subseteq \mathbb{R} $ is connected and contains only irrational numbers. We know that the only set which are connected in $\mathbb{R} $ are intervals. Since $X$ contains only irrational numbers, it must be singleton set. Thus, the cardinality of $X$ is $1$. Therefore, the correct option is (D).