1987 年

In the figure, $AB$, $BC$ and $CD$ are three equal chords of a circle. If $\angle BAC=a$, then $\angle AED=$

In the figure, $ABCD$ and $ABEF$ are parallelograms. $\dfrac{\text{Area of }ABCD}{\text{Area of }ABEF}=$

In the figure, I, II and III are equilateral triangles. Area of I : Area of II : Area of III $=$

Which of the following straight lines divide(s) the circle $(x-1)^2+(y+1)^2=1$ into two equal parts? I. $x-y-2=0$ II. $x+y+2=0$ III. $x-y+2=0$

The equation of a circle is $x^2+y^2-4x+2y+1=0$. Which of the following is/are true? I. The centre is $(-2,1)$. II. The radius is 2 units. III. The circle intersects the $y$-axis at two distinct points.

Two perpendicular lines $kx+y-4=0$ and $x-2y+3=0$ intersect at the point $(h,k)$. Find $h$ and $k$.

If the median of the 5 different integers $2$, $7$, $10$, $x$, $2x-3$ is $7$, then $x=$

The figures show the histograms of the three frequency distributions. Arrange their standard deviations in ascending order of magnitude.

One letter is taken from each of the words "MAN" and "ART" at random. Find the probability that the two letters are not the same.

Four persons $A$, $B$, $C$, $D$ sit randomly around a round table. The probability that $A$ sits next to $B$ is