1990 年

In the figure, $AC\parallel DE$, $FG\parallel BC$ and $AD:DF:FB=1:2:3$. If $BE=10$, find $FG$.

In the figure, $ABCDE$ is a regular pentagon. Find $\angle AFD$.

If the mean of the numbers $3, 3, 3, 3, 4, 4, 5, 5, 6, x$ is also $x$, which of the following is/are true? I. Mean = Median II. Mode = Range III. Median = Mode

Ten years ago, the mean age of a band of 11 musicians was 30. One of them is now leaving the band at the age of 40. What is the present mean age of the remaining 10 musicians?

There are 7 bags, 3 of which are empty and the remaining 4 each contains a ball. An additional ball is now put into one of the bags at random. After that a bag is randomly selected. Find the probability of selecting an empty bag.

$ABCD$ is a line segment. $AB:BC:CD=3:2:1$. If $A=(4,5)$, $D=(10,11)$, find $C$.

If the line $y=mx+b$ and $\dfrac{x}{a}+\dfrac{y}{b}=1$ are perpendicular, find $m$.

In the figure, the slopes of the straight lines $l_1$, $l_2$, $l_3$ and $l_4$ are $m_1$, $m_2$, $m_3$, $m_4$ respectively. Which of the following is true?

In the figure, a circle cuts the $x$-axis at two points 6 units apart. If the circle has centre $(4,5)$, then its equation is

The graph of $y=ax^2+bx+c$ is given as shown. Which of the following is/are true?

I. $a<0$ II. $b<0$ III. $c<0$