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

Which of the following is a source of rubber?

Efficiency of a heat engine whose sink is at a temperature of $300 ~K$ is $40 \%$. To increase the efficiency to $60 \%$,keeping the sink temperature constant,the source temperature must be increased by (in $~K$)

Let $u = i + j$,$v = i - j$ and $w = i + 2j + 3k$. If $n$ is a unit vector such that $u \cdot n = 0$ and $v \cdot n = 0$,then $|w \cdot n|$ is equal to

If $\sin (y+z-x), \sin (z+x-y)$ and $\sin (x+y-z)$ are in $AP$,then

Consider an ionic solid $M X$ with $NaCl$ structure. Construct a new structure $( Z )$ whose unit cell is constructed from the unit cell of $M X$ following the sequential instructions given below. Neglect the charge balance.

$(i)$ Remove all the anions ( $X$ ) except the central one

$(ii)$ Replace all the face centered cations $(M)$ by anions $(X)$

$(iii)$ Remove all the corner cations $(M)$

$(iv)$ Replace the central anion ( $X$ ) with cation $(M)$

The value of $\left(\frac{\text { number of anions }}{\text { number of cations }}\right)$ in $Z$ is. . . . .