From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable $$X$$ denote the number of defective items in the sample. If the variance of $$X$$ is $$\sigma^2$$, then $$96 \sigma^2$$ is equal to __________.

Suppose $$\mathrm{AB}$$ is a focal chord of the parabola $$y^2=12 x$$ of length $$l$$ and slope $$\mathrm{m}<\sqrt{3}$$. If the distance of the chord $$\mathrm{AB}$$ from the origin is $$\mathrm{d}$$, then $$l \mathrm{~d}^2$$ is equal to _________.

The number of ways of getting a sum 16 on throwing a dice four times is ________.

Let $$f$$ be a differentiable function in the interval $$(0, \infty)$$ such that $$f(1)=1$$ and $$\lim _\limits{t \rightarrow x} \frac{t^2 f(x)-x^2 f(t)}{t-x}=1$$ for each $$x>0$$. Then $$2 f(2)+3 f(3)$$ is equal to _________.