Refer to the botanical name of wheat "$Triticum\; aestivum$" and identify the statement which correctly describes it.

The function $f(x) = x e^{-x}, \forall x \in R$ attains a maximum value at $x$ equal to

Let $f(x)$ be defined for all $x > 0$ and be continuous. Let $f(x)$ satisfy $f(\frac{x}{y}) = f(x) - f(y)$ for all $x, y > 0$ and $f(e) = 1$. Then:

If the mean and the variance of a binomial variate $X$ are $2$ and $1$ respectively,then the probability that $X$ takes a value greater than or equal to one is

If $1$ is a multiple root of order $3$ for the equation $x^4-2x^3+2x-1=0$,then the other root is

The correct statements $(s)$ about intermolecular forces is$(are)$
$(A)$ The potential energy between two point charges approaches zero more rapidly than the potential energy between a point dipole and a point charge as the distance between them approaches infinity.
$(B)$ The average potential energy of two rotating polar molecules that are separated by a distance $r$ has $1 / r^3$ dependence.
$(C)$ The dipole-induced dipole average interaction energy is independent of temperature.
$(D)$ Nonpolar molecules attract one another even though neither has a permanent dipole moment.