Voltage phasors at the two terminals of a transmission line of length $$70$$ km have a magnitude of $$1.0$$ per unit but are $$180$$ degrees out of phase. Assuming that the maximum load current in the line is $$1/5$$^th of minimum $$3$$-phase fault current. Which one of the following transmission line protection schemes will NOT pick up for this condition?

Let x(t) be a periodic signal with time period T. Let y(t) = x(t - t₀) + x(t + t₀) for some t₀. The Fourier Series coefficient of y(t) are denoted by b_k. If b_k=0 for all odd k, then t₀ can be equal to

A function y(t) satisfies the following differential equation:$$$\frac{\operatorname dy\left(t\right)}{\operatorname dt}+\;y\left(t\right)\;=\;\delta\left(t\right)$$$ where $$\delta\left(t\right)$$ is the delta function. Assuming zero initial condition, and denoting the unit step function by u(t), y(t) can be of the form

Given X(z)=$$\frac z{\left(z-a\right)^2}$$ with $$\left|z\right|$$ > a, the residue of X(z)z^n-1 at z = a for n $$\geq$$ 0 will be