1993 年

In the figure, the radii of the sectors $OPQ$ and $ORS$ are $5\text{ cm}$ and $3\text{ cm}$ respectively. $\dfrac{\text{Area of shaded region}}{\text{Area of sector }OPQ}=$

Which of the following gives the compound interest on $\$10000$ at $6\%$ p.a. for one year, compounded monthly?

Originally $\dfrac{2}{3}$ of the students in a class failed in an examination. After taking a re-examination, $40\%$ of the failed students passed. Find the total pass percentage of the class.

Solve $\tan^4\theta+2\tan^2\theta-3=0$ for $0^\circ\le\theta<360^\circ$.

The figure shows the graph of the function

In the figure, $ABC$ is an equilateral triangle and the radii of the three circles are each equal to $1$. Find the perimeter of the triangle.

In the figure, $ABCDEFGH$ is a cuboid. The diagonal $AH$ makes an angle $\theta$ with the base $ABCD$. Find $\tan\theta$.

In the figure, if $\operatorname{arc}BC:\operatorname{arc}CA:\operatorname{arc}AB=1:2:3$, which of the following is/are true? I. $\angle A:\angle B:\angle C=1:2:3$ II. $a:b:c=1:2:3$ III. $\sin A:\sin B:\sin C=1:2:3$

In the figure, $TP$ and $TQ$ are tangents to the circle at $P$ and $Q$ respectively. If $M$ is a point on the minor arc $PQ$ and $\angle PMQ=\theta$, then $\angle PTQ=$

In the figure, $O$ is the centre of the circle. $AB$ touches the circle at $N$. Which of the following is/are correct? I. $M,\ N,\ K,\ O$ are concyclic. II. $\triangle HNB\sim\triangle NKB$ III. $\angle OAN=\angle NOB$