Consider ordinary differential equations given by $\dot{x}_1(t)=2 x_2(t), \dot{x}_2(t)=r(t)$ with initial conditions $x_1(0)=1$ and $x_2(0)=0$. If $r(t)=\left\{\begin{array}{ll}1, & t \geq 0 \\ 0, & t<0\end{array}\right.$, then $t=1, x_1(t)=$ _____________ (Round off to the nearest integer).

Let $C$ be a clockwise oriented closed curve in the complex plane defined by $|\lambda|=1$. Further, let $f(x)=j z$ be a complex function, where $j=\sqrt{-1}$. Then, $\oint_C f(z) d z=$ ___________ .

In the circuit with ideal devices, the power MOSFET is operated with a duty cycle of 0.4 in a switching cycle with $I=10 \mathrm{~A}$ and $V=15 \mathrm{~V}$. The power delivered by the current source, in $W$, is ________ . (round off to the nearest integer)

The 3-phase modulating waveforms $\left(v_a(t), v_b(t), v_c(t)\right)$, used in sinusoidal PWM in a voltage source inverter (VSI) are

$$ \begin{aligned} & v_a(t)=0.8 \sin (\omega t) \vee \\ & v_b(t)=0.8 \sin \left(\omega t-\frac{2 \pi}{3}\right) \vee \\ & v_c(t)=0.8 \sin \left(\omega t+\frac{2 \pi}{3}\right) \vee \end{aligned} $$

where $\omega=2 \pi \times 40 \mathrm{rad} / \mathrm{s}$ is the fundamental frequency. The modulating waveforms are compared with a 10 kHz triangular carrier whose magnitude varies between +1 and -1 . The VSI has a DC link voltage of 600 V and feeds a star connected motor. The per phase fundamental RMS motor voltage in volts is closest to