The value of $$\tan \frac{\pi}{8}$$ is

If $$B=\left[\begin{array}{lll}1 & \alpha & 2 \\ 1 & 2 & 2 \\ 2 & 3 & 3\end{array}\right]$$ is the adjoint of a $$3 \times 3$$ matrix A and $$|A|=5$$, then $$\alpha$$ is equal to

The logical statement $$[\sim(\sim p \vee q) \vee(p \wedge r)] \wedge(\sim q \wedge r)$$ is equivalent to

If $$w=\frac{z}{z-\frac{1}{3} i}$$ and $$|w|=1, i=\sqrt{-1}$$, then $$z$$ lies on