2005 年

Which of the regions in the figure may represent the solution of $\begin{cases}x\le2\\ x+y\ge2\\ x-y\ge0\end{cases}$ ?

If four arithmetic means are inserted between $12$ and $27$, then the sum of the four arithmetic means is

In the figure, $ACE$ and $BDF$ are straight lines. If the areas of the quadrilaterals $ABDC$ and $CDFE$ are $16\text{ cm}^2$ and $5\text{ cm}^2$ respectively, then the length of $AB$ is

For $0^\circ\le x\le360^\circ$, how many distinct roots does the equation $\cos x(\sin x-1)=0$ have?

$\sin(90^\circ-x)+\cos(x+180^\circ)=$

$\sin^2 1^\circ+\sin^2 3^\circ+\sin^2 5^\circ+\cdots+\sin^2 87^\circ+\sin^2 89^\circ=$

In the figure, $B$, $C$ and $D$ are three points on a horizontal plane such that $\angle CBD=90^\circ$. If $AB$ is a vertical pole, then $\angle BCD=$

In the figure, $VABCD$ is a right pyramid with a square base. If the angle between $VA$ and the base is $45^\circ$, then $\angle AVB=$

In the figure, $AB$ and $AC$ are tangents to the circle at $X$ and $Y$ respectively. $Z$ is a point lying on the circle. If $\angle BAC=100^\circ$, then $\angle XZY=$

In the figure, $O$ is the centre of the circle and $AOC$ is a straight line. If $AB$ and $BC$ are tangents to the circle such that $AB=3$ and $BC=4$, then the radius of the circle is