1991 年

A fair die is thrown $3$ times. The probability that "6" occurs exactly once is

If $(\sqrt{3}+1)\sqrt{x}=2$, then $x=$

If $\log x:\log y=m:n$, then $x=$

If $\mathrm{f}(x)=x-\dfrac{1}{x}$, then $\mathrm{f}(x)-\mathrm{f}\left(\dfrac{1}{x}\right)=$

If $p(x^2-x)+q(x^2+x)=4x^2+8x$, find $p$ and $q$.

If $x<0<y$, then which one of the following must be positive?

Which one of the following shaded regions represents the solution of $\begin{cases}2\le x+y\le 6\\0\le x\le 4\\0\le y\le 4\end{cases}$ ?

If $(x-2)(x-3)=(a-2)(a-3)$, solve for $x$.

If the sum to $n$ terms of an A.P. is $n^2+3n$, find the $7^{\text{th}}$ term of the A.P.

If $x$, $y$, $z$ are in G.P., which of the following must be true? I. $x+3,\ y+3,\ z+3$ are in G.P. II. $3x,\ 3y,\ 3z$ are in G.P. III. $x^2,\ y^2,\ z^2$ are in G.P.