Which one of the following elements on doping with germanium,makes it a $p$-type semiconductor?

If $x > 0$ and $x^y = e^{x-y}$,then $\frac{dy}{dx}$ is equal to

$64$ small drops of mercury,each of radius $r$ and charge $q$,coalesce to form a big drop. The ratio of the surface charge density of each small drop to that of the big drop is:

Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be

The curve satisfying the differential equation,$ydx - (x + 3y^2) dy = 0$ and passing through the point $(1, 1)$,also passes through the point

If $f(x) = \begin{cases} x \sin \frac{1}{x}, & x \ne 0 \\ k, & x = 0 \end{cases}$ is continuous at $x = 0$,then the value of $k$ is