Divergence of the $$3$$ $$-$$ dimensional radial vector field $$\overrightarrow r $$ is

A box contains $$4$$ white balls and $$3$$ red balls. In succession, two balls are randomly selected and removed from the box. Given that first removed ball is white, the probability that the $$2$$^nd removed ball is red is

For the differential equation $${{{d^2}x} \over {d{t^2}}} + 6{{dx} \over {dt}} + 8x = 0$$ with initial conditions $$x(0)=1$$ and $${\left( {{{dx} \over {dt}}} \right)_{t = 0}}$$ $$=0$$ the solution

Figure shows a composite switch consisting of a power transistor $$(BJT)$$ in series with a diode. Assuming that the transistor switch and the diode are ideal, the $$I$$-$$V$$ characteristic of the composite switch is