For the differential equation $${{{d^2}x} \over {d{t^2}}} + 6{{dx} \over {dt}} + 8x = 0$$ with initial conditions $$x(0)=1$$ and $${\left( {{{dx} \over {dt}}} \right)_{t = 0}}$$ $$=0$$ the solution

Given $$f\left( t \right) = {L^{ - 1}}\left[ {{{3s + 1} \over {{s^3} + 4{s^2} + \left( {k - 3} \right)}}} \right].$$
$$\mathop {Lt}\limits_{t \to \propto } \,\,f\left( t \right) = 1$$ then value of $$k$$ is

Figure shows a composite switch consisting of a power transistor $$(BJT)$$ in series with a diode. Assuming that the transistor switch and the diode are ideal, the $$I$$-$$V$$ characteristic of the composite switch is

The fully controlled thyristor converter in the figure is fed from a single-phase source. When the firing angle is $${0^ \circ }$$, the $$dc$$ output voltage of the converter is $$300V.$$ What will be the output voltage for a firing angle of $${60^ \circ }$$, assuming continuous conduction?