2. Let $a, b, c$ be any distinct positive numbers,
$$
x=\frac{b^{2}+1}{a}, y=\frac{c^{2}+1}{b}, z=\frac{a^{2}+1}{c} \text {. }
$$

Then the three numbers $x, y, z$ ( ).
(A) are all not greater than 2
(B) at least one is greater than 2
(C) are all not less than 2
(D) at least one is less than 2
2. B.

Notice that
$$
\begin{array}{l}
x y z=\frac{b^{2}+1}{a} \cdot \frac{c^{2}+1}{b} \cdot \frac{a^{2}+1}{c} \\
=\frac{b^{2}+1}{b} \cdot \frac{c^{2}+1}{c} \cdot \frac{a^{2}+1}{a} \\
=\left(a+\frac{1}{a}\right)\left(b+\frac{1}{b}\right)\left(c+\frac{1}{c}\right) .
\end{array}
$$

Since \(a, b, c\) are distinct positive numbers, we have
$$
a+\frac{1}{a} \geqslant 2, \quad b+\frac{1}{b} \geqslant 2, \quad c+\frac{1}{c} \geqslant 2,
$$

and the equality cannot hold simultaneously.
Therefore, \(x y z > 8\). Hence, at least one of \(x, y, z\) is greater than 2.