The area (in sq. units) of the region enclosed by $\{(x, y) \mid y \leq x^2, xy \leq 8, y \geq 1\}$ is...

The solution of the differential equation $\dfrac{dy}{dx} = \dfrac{x - y}{x + y}$, when $x = 0$ and $y = 0$ represents ....

The solution of the differential equation $\dfrac{dy}{dx} = \dfrac{a + bx}{c + dy}$ represents a family of circles centered at the origin if...

If $A(\vec{a})$, $B(\vec{b})$ and $C(\vec{c})$ are vertices of $\triangle ABC$. Point D divides segment BC internally in the ratio $2 : 1$. Point E divides segment AD internally in the ratio $1 : 2$, then the position vector of E is ____