$$C$$ is a closed path in the $$z-$$plane given by
$$\left| z \right| = 3.$$ The value of the integral
$$\oint\limits_c {{{{z^2} - z + 4j} \over {z + 2j}}dz} $$ is

A system is described by the following differential equation, where $$u(t)$$ is the input to the system and $$y(t)$$ is the output of the system. $$$\mathop y\limits^ \bullet \left( t \right) + 5y\left( t \right) = u\left( t \right)$$$

When $$y(0)=1$$ and $$u(t)$$ is a unit step function, $$y(t)$$ is

In the circuit shown in the figure, the value of capacitor C (in mF) needed to have critically damped response i(t) is ______.

A periodic variable x is shown in the figure as a function of time. The root - mean - square (rms) value of x is _______ .