Suppose the probability that a coin toss shows "head" is $p$, where $0 < p < 1$. The coin is tossed repeatedly until the first "head" appears. The expected number of tosses required is :

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)