1994 年

If the product of the first $n$ terms of the sequence $10, 10^2, 10^3, \dots, 10^n$ exceeds $10^{55}$, find the minimum value of $n$.

If $a:b=2:3$, $a:c=3:4$ and $a:d=4:5$, then $b:c:d=$

Let $x$ vary inversely as $\sqrt y$. If $y$ is increased by $69\%$, then $x$ will be

In the figure, $CDEF$ is a sector of a circle which touches $AB$ at $E$. If $AB=25$ and $BC=15$, find the radius of the sector.

In the figure, $AD:DB=1:2$, $AE:EC=3:2$. Area of $\triangle BDE$ : Area of $\triangle ABC=$

In the figure, area of $\triangle ABC$ : area of square $BCDE=2:1$. Find $PQ:BC$.

For $0^\circ\le x\le360^\circ$, how many roots does the equation $\sin x(\cos x+2)=0$ have?

The largest value of $(3\cos2\theta-1)^2+1$ is

In the figure, $\sin A:\sin B:\sin C=4:5:6$. If $AB=8$, find $AC$.

In the figure, $AB=p$, $\angle ACB=\theta$. Find $CD$.