$\lim _\limits{x \rightarrow 0} \frac{(1-\cos 2 x)(3+\cos x)}{x \tan 4 x}$ has the value

Let $a, b \in(a \neq 0)$. If the function $f$ is defined as

$$f(x)=\left\{\begin{array}{cc} \frac{2 x^2}{\mathrm{a}} & , 0 \leq x<1 \\ \mathrm{a} & , 1 \leq x<\sqrt{2} \\ \frac{2 \mathrm{~b}^2-4 b}{x} & , \sqrt{2} \leq x<\infty \end{array}\right.$$

is continuous in the interval $[0, \infty)$, then an ordered pair $(a, b)$ is

If $(p \wedge \sim q) \wedge(p \wedge r) \rightarrow \sim p \vee q$ is false, then the truth values of $p, q$ and $r$ are respectively

In $\triangle \mathrm{ABC}$, with usual notations, if $\mathrm{b}=3$, $c=8, \mathrm{~m} \angle \mathrm{~A}=60^{\circ}$, then the circumradius of the triangle is _______ units.