Suppose the circles $x^2+y^2=1$ and $(x-1)^2+(y-1)^2=r^2$ intersect each other orthogonally at the point $(u, v)$. Then $u+v=$ $\_\_\_\_$ .

In the open interval $(0,1)$, the polynomial $p(x)=x^4-4 x^3+2$ has

Consider the boost converter shown. Switch $Q$ is operating at 25 kHz with a duty cycle of 0.6 . Assume the diode and switch to be ideal. Under steady-state condition, the average resistance $R_{\text {in }}$ as seen by the source is $\_\_\_\_$ $\Omega$. (Round off to 2 decimal places)

A single-phase full bridge inverter fed by a 325 V DC produces a symmetric quasi-square waveform across " $a b$ " as shown. To achieve a modulation index of 0.8 , the angle $\theta$ expressed in degrees should be $\_\_\_\_$ . (Round off to 2 decimal places)

(Modulation index is defined as the ratio of the peak of the fundamental component of $V_{d b}$ to the applied DC value)