The area of the region $\{(x, y): |x-1| \leq y \leq \sqrt{5-x^{2}}\}$ is equal to:

If the area of the region enclosed by the curve $ay = x^2$ and the line $x + y = 2a$ is $ka^2$, then $k =$

The area bounded by the parabolas $y=x^2$ and $y=1-x^2$ is equal to

The parabola $y^2 = x$ divides the circle $x^2 + y^2 = 2$ into two parts whose areas are in the ratio

The area between the parabolas $x^2 = \frac{y}{4}$ and $x^2 = 9y$ and the straight line $y = 2$ is:

Let $C_{1}$ be the curve obtained by the solution of the differential equation $2xy \frac{dy}{dx} = y^{2} - x^{2}, x > 0$. Let the curve $C_{2}$ be the solution of $\frac{2xy}{x^{2} - y^{2}} = \frac{dy}{dx}$. If both the curves pass through $(1, 1)$,then the area enclosed by the curves $C_{1}$ and $C_{2}$ is equal to: