If the area enclosed between the curves $y^2 = 4kx$ and $y = kx, k > 0$ is $\dfrac{2k}{3}$ sq. units then $k = $

The solution of the differential equation $2x\dfrac{dy}{dx} - y = 3$ represents a family of

The solution of the differential equation $x\dfrac{dy}{dx} + y = x^3 y^6$, is...

If $\bar{a} = \hat{i} + \hat{j} + \hat{k}, \bar{b} = \hat{i} - \hat{j} + 2\hat{k}$ and $\bar{c} = x\hat{i} + (x - 2)\hat{j} - \hat{k}$ are three vectors in which $\bar{c}$ lies in the plane of $\bar{a}$ and $\bar{b}$, then $x = \cdots$