In the figure shown, assume the op-amp to be ideal. Which of the alternatives gives the correct Bode plots for the transfer function $${{{V_O}\left( \omega \right)} \over {{V_i}\left( \omega \right)}}?$$

In the Wien Bridge oscillator circuit shown in figure, the bridge is balanced when

For the given system, it is desired that the system be stable. The minimum value of $$\alpha $$ for this condition is _________

The Bode magnitude plot of the transfer function $$G\left( s \right) = {{K\left( {1 + 0.5s} \right)\left( {1 + as} \right)} \over {s\left( {1 + {s \over 8}} \right)\left( {1 + bs} \right)\left( {1 + {s \over {36}}} \right)}}$$ is shown below: Note that $$-6$$ $$dB/octave=-20$$ $$dB/decade.$$ The value of $${a \over {bK}}$$ is _______.