If $\tan x$ is an integrating factor of the differential equation $\dfrac{dy}{dx} + Py = Q$, then $P$ can be

The order and degree of the differential equation $\left(\dfrac{d^3 y}{dx^3}\right)^{\frac{2}{3}} - 3\dfrac{d^2 y}{dx^2} + 5\dfrac{dy}{dx} + 4 = 0$ are respectively

Let $\bar{a} = \hat{i} + \hat{j} + \hat{k}$, $\bar{b} = \hat{i} - 3\hat{j} + 2\hat{k}$ and $\bar{c} = 3\hat{i} - 2\hat{k}$. If a vector $\bar{p}$ satisfies the conditions $\bar{p} \cdot \bar{c} = 0$ and $\bar{p} \times \bar{a} = \bar{b} \times \bar{a}$, then the value of $|\bar{p}| = $...

The volume of the tetrahedron whose vertices are A$(-1, 2, 3)$, B$(3, -2, 1)$, C$(p, 1, 3)$, D$(-1, -2, 4)$ is $\dfrac{16}{3}$ cubic units then the value of p is