1989 年

In the figure, $ABCDE$ is a regular pentagon and $ABYE$ is a rhombus. Find $\angle CAY$.

Referring to the figure, find the length of the line segment joining $P$ and $Q$.

In the figure, $O$ is the centre of two concentric circles. $ADOEB$ and $CGFB$ are straight lines. Which of the following is/are true?

I. $AC /\!/ DG$ II. $BF=CG$ III. $A$, $E$, $F$ and $C$ are concyclic

In the figure, $TC$ is a tangent to the circle at $C$ and $AB /\!/ DC$. If $\angle BCT=48^\circ$, then $\theta=$

Referring to the data 1, 1, 1, 1, 1, 2, 2, 2, 3, which of the following is/are true?

I. median $<$ mean II. range $=3$ III. mode $=3$

A biased die is thrown. Suppose the probabilities of getting 1, 2, 3, 4 and 5 are respectively $\dfrac{1}{2}$, $\dfrac{1}{4}$, $\dfrac{1}{8}$, $\dfrac{1}{16}$ and $\dfrac{1}{32}$. What is the probability of getting 6?

A bag contains 4 red, 3 green and 2 white balls. Three men $A$, $B$ and $C$ each draw one ball in turn from the bag at random without replacement. If $A$ draws first, $B$ second and $C$ third, what is the probability that the balls drawn by $B$ and $C$ are both white?

The equation of the straight line perpendicular to $2x+y-3=0$ and passing through $(1,-1)$ is

In the figure, the line $ax-2y+5=0$ passes through the point $(3,4)$. What is the area of the shaded part?

In the figure, $C$ is the centre of the circle $x^2+y^2-8x-7y+12=0$. If the circle cuts the $x$-axis at $A$ and $B$, find the area of $\triangle CAB$.