Let $A = \{(x, y) : y^2 \le 4x, y - 2x \ge -4\}$. The area of the region $A$ is

The area (in sq. units) of the part of the circle $x^{2} + y^{2} = 36$ which is outside the parabola $y^{2} = 9x$ is:

Let the area of the region $\{(x, y): 2y \leq x^2+3, y +|x| \leq 3, y \geq|x-1|\}$ be $A$. Then $6A$ is equal to:

For $a>0$, let the curves $C_1: y^2=a x$ and $C _2: x ^2=$ ay intersect at origin O and a point P Let the line $x = b (0 < b < a )$ intersect the chord $O P$ and the x -axis at points Q and R , respectively. If the line $x=b$ bisects the area bounded by the curves, $C _1$ and $C _2$, and the area of $\Delta OQR =\frac{1}{2}$, then ' $a$ ' satisfies the equation

The area (in sq. units) of the region $\{x \in R : x \ge 0, y \ge 0, y \ge x - 2, \text{ and } y \le \sqrt{x}\}$ is

The area of the region bounded by the curves $x + 3y^2 = 0$ and $x + 4y^2 = 1$ is equal to: (in $/3$)