A $$10{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$ digit timer counter possesses a base clock of frequency $$100$$ $$MHz$$. When measuring a particular input, the reading obtained is the same in: (i) Frequency mode of operation with a gating time of one second and (ii) Period mode of operation (in the $$ \times \,\,\,10$$ ns scale). The frequency of the unknown input (reading obtained) in $$Hz$$ is _______.

A $$3$$-phase, $$2$$-pole, $$50$$ $$Hz,$$ synchronous generator has a rating of $$250$$ $$MVA,$$ $$0.8$$ $$pf$$ lagging. The kinetic energy of the machine at synchronous speed is $$100$$ $$MJ.$$ The machine is running steadily at synchronous speed and delivering $$60$$ $$MW$$ power at a power angle of $$10$$ electrical degrees. If the load is suddenly removed, assuming the acceleration is constant for $$10$$ cycles, the value of the power angle after $$5$$ cycles is ________ electrical degrees.

Two generating units rated $$300$$ $$MW$$ and $$400$$ $$MW$$ have governor speed regulation of $$6\% $$ and $$4\% $$ respectively from no load to full load. Both the generating units are operating in parallel to share a load of $$600$$ $$MW.$$ Assuming free governor action, the load shared by the larger unit is _______ $$MW.$$

A $$25$$ $$kVA,$$ $$400$$ $$V,$$ $$\Delta $$ - connected, $$3$$-phase, cylindrical rotor synchronous generator requires a field current of $$5$$ $$A$$ to maintain the rated armature current under short-circuit condition. For the same field current, the open-circuit voltage is $$360$$ $$V.$$ Neglecting the armature resistance and magnetic saturation, its voltage regulation (in $$\% $$ with respect to terminal voltage), when the generator delivers the rated load at $$0.8$$ $$pf$$ leading, at rated terminal voltage is ____________.