The power input to a $500 \mathrm{~V}, 50 \mathrm{~Hz}, 6$ pole, 3 phase induction motor running at 975 rpm is 40 kW . The stator losses are 1 kW . If the total friction and windage losses are 2.025 kW , then the efficiency is

$\_\_\_\_$ $\%$.

A belt-driven DC shunt generator running at 300 rpm delivers 100 kW to a 200 V DC grid. It continues to run as a motor when the belt breaks, taking 10 kW from the DC grid. The armature resistance is $0.025 \Omega$, field resistance is $50 \Omega$ and brush drop is 2 V . Ignoring armature reaction, the speed of the motor is _________ rpm. (Round off to 2 decimal places.)

An alternator with an internal voltage of $1 \delta_1$ pu and synchronous reactance of 0.4 pu is connected by a transmission line of reactance 0.1 pu to a synchronous motor having synchronous reactance 0.35 pu and internal voltage of $0.85 \delta_2 \mathrm{pu}$. If the real power supplied by the alternator is 0.866 pu , then ( $\delta_1-\delta_2$ ) is $\_\_\_\_$ degrees (Round off to 2 decimal places). (Machines are of non-salient type. Neglect resistances)

Which one of the following vector functions represents a magnetic field $\vec{B}$ ? ( $\hat{x}, \hat{y}$, and $\hat{z}$ are unit vectors along $x$-axis, $y$-axis and $z$-axis respectively)