Two resistors with nominal resistance values $${R_1}$$ and $${R_2}$$ have additive uncertainties $$\Delta {R_1}$$ and $$\Delta {R_2},$$ respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance $$R$$ is

A stationary closed Lissajous pattern on an oscilloscope has $$3$$ horizontal tangencies and $$2$$ vertical tangencies for a horizontal input with frequency $$3$$ $$kHZ.$$ The frequency of the vertical input is

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.