1984 年

In the figure, $AB=x$ and $AC=2x$. The area of $\triangle ABC$ is 16. $x$ (correct to 2 decimal places) is

The sum of the interior angles of a convex polygon is greater than the sum of the exterior angles by $360^\circ$. How many sides has the polygon?

In the figure, $x=$ ?

In the figure, $O$ is the centre of the circle. $TA$ and $TB$ touch the circle at $A$ and $B$ respectively. $OA=2$. The length of the arc $APB$ is

The point $P$ divides $AB$ internally so that $AP:PB=2:1$. The coordinates of $A$ and $B$ are $(x_1,y_1)$ and $(x_2,y_2)$ respectively. The coordinates of $P$ are

The line $x+y+k=0$ ($k$ being a constant) passes through the centre of the circle $x^2+y^2-2x+4y-6=0$. $k=$

The equation of a circle is $x^2+y^2-2x+5y-7=0$. Which of the following is/are true? I. The circle passes through the point $(-1,1)$. II. The centre of the circle lies in the second quadrant. III. The circle intersects the $x$-axis at two points.

If $a$, $b$ and $c$ are positive real numbers, which of the following graphs could represent the line $ax+by+c=0$?

The probability that John will win a game is $\dfrac13$ and the probability that he will lose is $\dfrac23$. What is the probability that, in three games, he will win any two games and lose one game?

Two dice are thrown. What is the probability of getting a sum of 8?