Consider the differential equation $${x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - y = 0.\,\,$$ Which of the following is a solution to this differential equation for $$x > 0?$$

All the values of the multi valued complex function $${1^i},$$ where $$i = \sqrt { - 1} $$ are

The $$SCR$$ in the circuit shown has a latching current of $$40$$ $$mA.$$ A gate pulse of $$50$$ $$\mu s$$ is applied to the $$SCR$$. The maximum value of $$R$$ in $$\Omega $$ to ensure successful firing of the $$SCR$$ is ____________.

A fully controlled converter bridge feeds a highly inductive load with ripple free load current. The input supply $$\left( {{V_s}} \right)$$ to the bridge is a sinusoidal source. Triggering angle of the bridge converter is $$\,\alpha = {30^0}.$$ The input power factor of the bridge is ____________.