If the area bounded by the curve $x^2 = by$ and the lines $y = 1, y = 4$ in the first quadrant is $28$ sq. units, then the value of $b$ is...

If the area bounded by the curve $x^2y + y^2x = \alpha xy$ is $2$ units,then the possible value$(s)$ of $\alpha$ is/are:

The area of the region bounded by the line $y = 3 - x$,the $X$-axis,and the lines $x = 2$ and $x = 5$ is . . . . . . .

Let $z=x+iy$ be a complex number $(x, y \in R)$. Let $A$ and $B$ be two sets such that $A=\{z:|z| \leq 2\}$ and $B=\{z:(z+2y)+\bar{z} \geq 4\}$. The area of region $A \cap B$ is

The area of the region bounded by the parabola $y^2 = 12x$ and its latus rectum is . . . . . . sq. units.

The area of the region bounded by the curve $y=2x-x^2$ and the line $y=x$ is . . . . . . square units.