1992 年

If a polynomial $\mathrm{f}(x)$ is divisible by $x-1$, then $\mathrm{f}(x-1)$ is divisible by

Find the $(2n)$th term of the G.P. $-\dfrac{1}{2},\ 1,\ -2,\ 4,\ \ldots$

If the price of an orange rises by $\$1$, then $5$ fewer oranges could be bought for $\$100$. Which of the following equations gives the original price $\$x$ of an orange?

By selling an article at $10\%$ discount off the marked price, a shop still makes $20\%$ profit. If the cost price of the article is $\$19\,800$, then the marked price is

Coffee $A$ and coffee $B$ are mixed in the ratio $x:y$ by weight. $A$ costs $\$50$/kg and $B$ costs $\$40$/kg. If the cost of $A$ is increased by $10\%$ while that of $B$ is decreased by $15\%$, the cost of the mixture per kg remains unchanged. Find $x:y$.

In the figure, find $\tan\theta$.

In the figure, if $\theta$ is the angle between the diagonals $AG$ and $BH$ of the cuboid, then

In the figure, $OA$ is perpendicular to the plane $ABC$. $OA=AB=AC=2\text{ cm}$ and $BC=2\sqrt2\text{ cm}$. If $M$ and $N$ are the mid-points of $OB$ and $OC$ respectively, find the area of $\triangle AMN$.

In $\triangle ABC$, $\angle A=30^\circ$, $c=6$. If it is possible to draw two distinct triangles as shown in the figure, find the range of values of $a$.

In the figure, the two circles touch each other at $C$. The diameter $AB$ of the bigger circle is tangent to the smaller circle at $D$. If $DE$ bisects $\angle ADC$, find $\theta$.