1987 年

A die is thrown twice. Find the probability that the number obtained at the first throw is greater than that at the second throw.

If $a:b=3:2$, $b:c=4:3$, then $a+b:b+c=$

Peter bought an article for $\$x$. He sold it to Mary at a profit of $20\%$. Mary then sold it to John for $\$90$ at a loss of $25\%$. Find $x$.

If $x$ and $y$ are integers with $x>y$, which of the following is/are true? I. $x^2>y^2$ II. $\dfrac{1}{x}<\dfrac{1}{y}$ III. $10^x>10^y$

Solve the inequality $x\log_{10}0.1>\log_{10}10$.

If $x^2+y^2=5$ and $x+y=3$, then $x-y=$

Find the H.C.F. of $(2x-1)(x^2-6x+9)$ and $(x^2-3x)(4x^2-1)$.

If $a$ is $10\%$ less than $b$ and $b$ is $10\%$ greater than $c$, then $a:c=$

If $3a=2b=5c$, then $\dfrac{1}{a}:\dfrac{1}{b}:\dfrac{1}{c}=$

A man walks from place $A$ to place $B$ at a speed of $3\text{ km/h}$ and cycles immediately back to place $A$ along the same road at a speed of $15\text{ km/h}$. The average speed for the whole trip is