The open loop transfer function of a unity feedback system is given by G(s)=$${{3{e^{ - 2s}}} \over {s\left( {s + 2} \right)}}.$$ The gain and phase crossover frequencies in rad/sec are, respectively

A double integrator plant, $$G(s) = {K \over {{s^2}}},H(s) = 1$$ is to be compensated to achieve the damping ratio $$\zeta = 0.5$$ and an undamped natural frequency, $${\omega _n} = 5$$ rad/sec. Which one of the following compensator $${G_c}(s)$$ will be suitable?

The Boolean function f implemented in the figure using two input multiplexers is

The transistors used in a portion of the TTL gate shown in figure have β=100. the base-emitter voltage of is 0.7V for a transistor in active region and 0.75V for a transistor in saturation . If the sink current I=1mA and the output is at logic 0, then the current $${I_R}$$ I will be equal to