1993 年

A group of $n$ numbers has mean $m$. If the numbers $1$, $2$ and $6$ are removed from the group, the mean of the remaining $n-3$ numbers remains unchanged. Find $m$.

The figure shows the frequency polygons of two symmetric distributions $A$ and $B$ with the same mean. Which of the following is/are true? I. Interquartile range of $A$ < interquartile range of $B$ II. Standard deviation of $A$ > standard deviation of $B$ III. Mode of $A$ > mode of $B$

If $9^{x+2}=36$, then $3^x=$

If $a:b=2:3$ and $b:c=5:3$, then $\dfrac{a+b+c}{a-b+c}=$

$\begin{array}{|c|c|}\hline x & \text{Sign of } \mathrm{f}(x)\\\hline 3.56 & +\\\hline 3.58 & -\\\hline 3.57 & +\\\hline 3.575 & +\\\hline\end{array}$ From the table, a root of the equation $\mathrm{f}(x)=0$ is

Given that the positive numbers $p,\ q,\ r,\ s$ are in G.S., which of the following must be true? I. $kp,\ kq,\ kr,\ ks$ are in G.S., where $k$ is a non-zero constant. II. $a^p,\ a^q,\ a^r,\ a^s$ are in G.S., where $a$ is a positive constant. III. $\log p,\ \log q,\ \log r,\ \log s$ are in A.S.

In the figure, the rectangle has perimeter $16\text{ cm}$ and area $15\text{ cm}^2$. Find the length of its diagonal $AC$.

In factorizing the expression $a^4+a^2b^2+b^4$, we find that

If the solution of the inequality $x^2-ax+6\le 0$ is $c\le x\le 3$, then

In the figure, $ABCD$ is a square and $ABE$ is an equilateral triangle. $\dfrac{\text{Area of }ABE}{\text{Area of }ABCD}=$