If the difference between the expectation of the square of a random variable $\left(E\left[X^2\right]\right)$ and the square of the expectation of the random variable $\left(E[X]\right)^2$ is denoted by $R$, then

The quantity $R$ is defined as:

By definition, this is the variance of the random variable $X$, denoted by $\text{Var}(X)$:

Since $(X - E[X])^2 \ge 0$ for all real values of $X$, the expectation of a non-negative quantity must also be non-negative:

$R$ equals $0$ when $X$ is a constant almost surely, and $R > 0$ otherwise. Thus, the general condition is $R \ge 0$.

Hence, option (C) is correct.