Let $(x, y) \in \Re^2$. The rate of change of the real valued function, $V(x, y)=x^2+x+y^2+1$ at the origin in the direction of the point $(1,2)$ is _________ (round off to the nearest integer)

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)