The area (in sq. units) of the region described by $\left\{(x, y) / y^2 \leq 2 x\right.$ and $\left.y \geq(4 x-1)\right\}$ is

Let $y=y(x)$ be the solution of the differential equation $(x \log x) \frac{d y}{d x}+y=2 x \log x(x \geq 1)$ then $y(\mathrm{e})$ is equal to

The set of all points, for which $f(x)=x^2 e^{-x}$ strictly increases, is

Range of the function $\mathrm{f}(x)=\frac{x^2+x+2}{x^2+x+1}, x \in \mathbb{R}$ is