For what values of $$'a'$$ does the system shown in figure have a zero steady state error $$\left[ {i.e.,\mathop {Lim}\limits_{t \to \infty } \,\,E\left( t \right)} \right]$$ for a step input?

For what range of $$K$$ is the following system (Figure) asymptotically stable Assume $$K \ge 0$$

Which of the following figure(s) represent valid root loci in the $$s$$ - plane for positive $$K?$$ Assume that the system has transfer function with real coefficient.

A unity feedback system has the open loop transfer function $$G\left( s \right) = {1 \over {\left( {s - 1} \right)\left( {s + 2} \right)\left( {s + 3} \right)}}$$
The Nyquist plot of $$G$$ encircle the origin