The number of solutions of $log _{\frac{1}{5}}log_{\frac{1}{2}}(\left | z \right |^{2}+4\left | z \right |+3)< 0$ is/are?

If $a, b, c, d$ be a form consecutive term of an increasing A.P., then the roots of the equation $\left( {x - a} \right)\left( {x - c} \right) + 2\left( {x - b} \right)\left( {x - d} \right) = 0$

If $z = x+iy$ and $w = \dfrac{(1-iz)}{(z-i)}$, then $|w| = 1$ implies that, in the complex plane

If z be a complex number satisfying$\displaystyle\ z^{4}+z^{3}+2z^{2}+z+1=0$ then $\displaystyle\ |z|$ is