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 120 V DC shunt motor takes 2 A at no load. It takes 7 A on full load while running at 1200 rpm. The armature resistance is 0.8 Ω, and the shunt field resistance is 240 Ω. The no load speed, in rpm, is _________.

A 220 V, 10 kW, 900 rpm separately excited DC motor has an armature resistance R_a= 0.02 Ω. When the motor operates at rated speed and with rated terminal voltage, the electromagnetic torque developed by the motor is 70 Nm. Neglecting the rotational losses of the machine, the current drawn by the motor from the 220 V supply is