1. (2000 Hebei Province Competition Question) When $0<x \leqslant 1$, which of the following inequalities is correct? $(\quad$ ).
A. $\frac{\sin x}{x}<\left(\frac{\sin x}{x}\right)^{2} \leqslant \frac{\sin x^{2}}{x^{2}}$
B. $\left(\frac{\sin x}{x}\right)^{2}<\frac{\sin x}{x} \leqslant \frac{\sin x^{2}}{x^{2}}$
C. $\left(\frac{\sin x}{x}\right)^{2}<\frac{\sin x^{2}}{x^{2}} \leqslant \frac{\sin x}{x}$
D. $\frac{\sin x^{2}}{x^{2}} \leqslant\left(\frac{\sin x}{x}\right)^{2}<\frac{\sin x}{x}$
1. Choose B. Reason: Consider the familiar relation $\sin x \leqslant x$. Since $0\left(\frac{\sin x}{x}\right)^{2}$. Also, because $f(x)=\frac{\sin x}{x}$ is a decreasing function on $\left(0,-\frac{\pi}{2}\right)$, and $0<x^{2} \leqslant x \leqslant 1<\frac{\pi}{2}$, it follows that $\frac{\sin x^{2}}{x^{2}} \geqslant$ $\frac{\sin x}{x}$.