If the function $f(x)=\left\{\begin{array}{cl}\frac{\cos a x-\cos b x}{\cos c x-\cos b x} & , \text { if } x \neq 0 \\ -1 & , \text { if } x=0\end{array}\right.$ is continuous at $x=0$, then $\mathrm{a}^2, \mathrm{~b}^2, \mathrm{c}^2$ are in

$$ \int_0^1 \tan ^{-1} x d x= $$

If the truth value of the expression $[(p \vee q) \wedge(q \rightarrow r) \wedge(\sim r)] \rightarrow(p \wedge q)$ is False, then truth values of $p, q, r$ are respectively.

Consider statements $\mathrm{p}: \mathrm{S}_1$ is closed; $\mathrm{q}: \mathrm{S}_2$ is closed; $\mathrm{r}: \mathrm{S}_3$ is closed. The simplified equivalent circuit diagram and its logical statement for the switching circuit is respectively.