1982 年

$\$9000$ is divided among $A$, $B$ and $C$. $A$'s share, $B$'s share and $C$'s share, in that order, form an arithmetic progression. If $B$'s share is three times $A$'s share, how much does $C$ get?

$1,-0.1,0.01,-0.001,\dots$ is a geometric progression. What is its sum to infinity?

If $x\ne0$, which of the following is/are geometric progression? I. $x, x^2, x^3, x^4$ II. $x, 2x, 3x, 4x$ III. $x, -x^2, x^3, -x^4$

The average of $x$ and $y$ is $a$, the average of $y$ and $z$ is $b$, and the average of $x$ and $z$ is $c$. What is the average of $x$, $y$ and $z$?

In the figure an equilateral triangle is inscribed in a circle of radius $a$. What is the area of the triangle?

Four identical trapeziums, each of area $16\text{ cm}^2$, are drawn inside a square of side $10\text{ cm}$ as shown in the figure. What is the height of each trapezium?

The perimeter of the given figure $ABCDE$ is $2(\pi+4)\text{ cm}$. The upper portion $AED$ is a semi-circle and the lower portion $ABCD$ is a rectangle. $AB:BC=1:2$. What is the area of the given figure?

In the figure, the rectangles are similar. $PQ=a$, $QR=b$. If $AC=2PR$, what is the area of $ABCD$?

The above figure shows the graph of $y=a\cos x+1$ for $0\le x\le\pi$. $a=$

$\dfrac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}+\dfrac{\sin\theta-\cos\theta}{\sin\theta+\cos\theta}=$