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

Let $S$ be a non-empty subset of $\mathbb{R}$. Consider the following statement:

p : There is a rational number $x \in \mathrm{~S}$ such that $x>0$.

Which of the following statements is the negation of the statement p?

The number of values of $x$ in the interval $(0,5 \pi)$ satisfying the equation $3 \sin ^2 x-7 \sin x+2=0$