Consider the transformer connections in a part of a power system shown in the figure. The nature of transformer connections and phase shifts are indicated for all but one transformer. Which of the following connections, and the corresponding phase shift $$\theta ,$$ should be used for the transformer between $$A$$ and $$B$$?

Single line diagram of a $$4$$-bus single source distribution system is shown below. Branches $${e_1},\,\,$$ $${e_2},\,\,$$ $${e_3}\,\,$$ and $${e_4}\,\,$$ have equal impedences. The load current values indicated in the figure are in per unit.

Distribution Company's policy requires radial system operation with minimum loss. This can be achieved by opening of the branch

The total reactance and total susceptance of a lossless overhead $$EHV$$ line, operating at $$50$$ $$Hz,$$ are given by $$0.045$$ pu and $$1.2$$ pu respectively. If the velocity of wave propagation is $$3\,\, \times \,\,{10^5}$$ km/s, then the approximate length of line is

Let a signal $${a_1}\,\sin \left( {{\omega _1}t + {\phi _1}} \right)$$ be applied to a stable linear time-invariant system. Let the corresponding steady state output be represented as $${a_2}F\left( {{\omega _2}t + {\phi _2}} \right).$$ Then which of the following statements is true?