$1-$A large $3-$phase. $4000$ V$.60$ Hz squirrel cage induction motor draws a current of $385$ A and a total active power of $2344$ kW when operating at full$-$load. The corresponding speed is accurately measured and is found to be $709\mathrm{.}2$ r$/$min$.$ The stator is connected in wye and the resistance between two stator terminals is $0\mathrm{.}10$ Q$.$ The total iron losses are $23\mathrm{.}4$ kW and the windage and friction losses arc $12$ kW$.$ Calculate the following:

a$.$ The power factor at full$-$load

b$.$ The active power supplied lo the rotor

c$.$ The total I$\text{'}$R losses in the rotor

d$.$ The load mechanical power $[$kW$],$ torque $[$kNm$],$ and efficiency $[\%]$