Area enclosed by curve $y = 2x^2$ and lines $x \geq 1,\ y \leq 4$ is ..... sq. units

If $y = e^{-mx}$ is a solution of the differential equation $\dfrac{d^2y}{dx^2} + 4\dfrac{dy}{dx} + 3y = 0$, then the values of $m$ are

For the differential equation $(x^2 + y^2)\,dy = xy\,dx$, it is given that $y(1) = 1$ and $y(x_0) = e$, then the value of $x_0$ is _____

In $\triangle OAB$, $O(0,0,0),\ A(6,2,-3)$ and $B(4,0,3)$ are the vertices. Let $\vec{a}$ and $\vec{b}$ be position vectors of points $A$ and $B$ respectively and $OM$ is the projection of $\vec{a}$ on $\vec{b}$ then $l(AM)$ is equal to...