A 3-phase Inductor Motor is driving a constant torque load at rated voltage and frequency. If both voltage and frequency are halved, following statements relate to the new condition if stator resistance, leakage reactance and core loss are ignored.
P. The difference between synchronous speed and actual speed remains same
Q. The air-gap flux remains same
R. The stator current remains same
S. The p.u. slip remains same
Among the above, correct statements are

No-load test on a 3-phase induction motor was conducted at different supply voltages and a plot of input power versus voltage was drawn. This curve was extrapolated to intersect the y-axis. This intersection point yields

Group I lists different applications and Group II lists the motors for these applications. Match the application with the most suitable motor and choose the right combination among the choices given there after:

Group I
P. Food mixer
Q. Cassette tape recorder
R. Domestic water pump
S. Escalator

Group II
1. Permanent magnet dc motor
2. Single phase induction motor
3. Universal motor
4. Three phase induction motor
5. DC series motor
6. Stepper motor

Figure shows an ideal three-winding transformer. The three windings 1,2,3 of the transformer are wound on the same core as shown. The turn's ratio N₁:N₂:N₃ is 4:2:1. A resistor of 10 Ω is connected across winding-2. A capacitor of reactance 2.5 Ω is connected across winding-3. Winding-1 is connected across a 400 V, ac supply. If the supply voltage phasor $$\overline V=400\angle0^\circ$$, the supply current phasor $${\overline I}_1$$ is given by