The figure show the per-phase representation of a phase-shifting transformer connected between buses $$1$$ and $$2,$$ where $$\alpha $$ is a complex number with non-zero real and imaginary parts.
For the given circuit, $${Y_{bus}}$$ and $${Z_{bus}}$$ are bus admittance matrix and bus impedance matrix, respectively, each of size $$2\, \times \,2$$. Which one of the following statements is true?

Consider an overhead transmission line with $$3$$-phase, $$50$$ $$Hz$$ balanced system with conductors located at the vertices of an equilateral triangle of length $$\,{D_{ab}} = {D_{bc}} = {D_{ca}} = 1\,\,\,$$ m as shown in figure below. The resistance of the conductors are neglected. The geometric mean radius (GMR) of each conductor is $$0.01$$ $$m$$. Neglect the effect of ground, the magnitude of positive sequence reactance in $$\,\Omega $$/$$km$$ (rounded off to three decimal places) is ________________.

The normal - $$\pi $$ circuit of a transmission line is shown in the figure.

Impedance $$Z = 100\angle {80^ \circ }$$ and reactance $$\,X = 3300\Omega .$$ The magnitude of the characteristic impedance of the transmission line, in $$\Omega ,$$ is ________. (Give the answer up to one decimal place.)

A cascade system having the impulse responses $$$\begin{array}{l}h_1\left(n\right)=\left\{1,\;-1\right\}\;\;\;and\;\;h_2\left(n\right)=\left\{1,\;1\right\}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\end{array}$$$ is shown in the figure below, where symbol $$\uparrow$$ denotes the time origin. The input sequence x(n) for which the cascade system produces an output sequence $$$\begin{array}{l}y\left(n\right)=\left\{1,\;2,\;1,\;-1,\;-2,\;-1\right\}\;\;is\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\end{array}$$$