1997 年

In the figure, $ABCD$ is a rectangle inclined at an angle of $45^\circ$ to the horizontal plane $BCEF$. Find the inclination of $AC$ to the horizontal plane correct to the nearest degree.

In the figure, $CD=$

For $0\le\theta\le2\pi$, how many roots does the equation $\tan\theta(\tan\theta-2)=0$ have?

In the figure, $\mathrm{f}(x)=$

The equation of a circle is given by $x^2+y^2-4x+6y-3=0$. Which of the following statements is/are true? I. The centre of the circle is $(-2,3)$. II. The radius of the circle is $4$. III. The origin is inside the circle.

A circle has $(a,0)$ and $(0,b)$ as the end points of a diameter. Which of the following points lie(s) on this circle? I. $(-a,-b)$ II. $(0,0)$ III. $(a,b)$

In the figure, $AEB$ and $ADC$ are straight lines. $ED\parallel BC$ and $ED:BC=2:3$. If the coordinates of $A$ and $B$ are $(4,7)$ and $(0,1)$ respectively, find the coordinates of $E$.

In the figure, $OXY$ is a sector with centre $O$. If $Z$ is the mid-point of $YO$, find area of $\triangle OXZ$ : area of sector $OXY$.

In the figure, the rocket model consists of three parts. Parts I and III can be joined together to form a right circular cone. Part II is a right cylinder. Find the volume of the rocket model.

In the figure, $AC$ is the angle bisector of $\angle BAD$. Which of the following statements must be true? I. $\triangle BCE\sim\triangle ADE$ II. $\triangle ABC\sim\triangle AED$ III. $\triangle ABC\sim\triangle BDA$