A $440$ V$,50$ Hz$,2-$pole, Y$-$connected induction motor is rated at $100$ hp$.$ Its equivalent circuit components have the following values: $($R$1=0\mathrm{.}075$ ohm, X$1=0\mathrm{.}17$ ohm$)$; $($R$2=0\mathrm{.}065$ ohm, X$2=0\mathrm{.}17$ ohm$)$; Xm $=7\mathrm{.}2$ ohm. Rotor slip is $4\%$ at the rated voltage and frequency. Mechanical and core losses are $1\mathrm{.}0$ KW and $1\mathrm{.}10$ KW respectively. Find $($a$)$ rotor speed $($b$)$ line current and motor p$.$f $($c$)$ Air$-$gap and converted power $($d$)$ Induced torque.