A slip$-$ring induction motor with a nameplate indicating $5$ HP$,380$ V$,50$ Hz$,3-$phase, $750$ RPM has the following equivalent circuit parameters for each phase as seen by the stator:

R$1=11\mathrm{.}4,$X$1=8\mathrm{.}6,$ X$2=168,$ R$2=4\mathrm{.}3,$ XM$=200$

Given that the rated speed is $720$RPM$,$ calculate the following:

a$)$ Number of poles and slip at rated speed

b$)$ Starting stator current and stator current at rated speed

c$)$ Starting torque and torque at rated speed

d$)$ Maximum torque, slip, and speed at which maximum torque occurs

e$)$ Rotor resistance required for maximum torque to occur at starting

f$)$ Input power, output power, power factor, and efficiency at rated speed