A thin soap bubble of radius R = 1 cm, and thickness a = 3.3 µm(a << R), is at a potential of 1 V with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop of soap (assuming all the soap is contained in the drop) of radius r. The volume of the soap in the thin bubble is $$4\mathrm{πR}^2\mathrm a$$ and that of the drop is $$\frac43\mathrm{πr}^3$$. The potential in volts, of the resulting single spherical drop with respect to the same reference point at infinity is __________. (Give the answer up to two decimal places.)

Consider a solid sphere of radius 5 cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed.

The figures show diagrammatic representations of vector fields $$\overrightarrow X,\;\overrightarrow Y,\;and\;\overrightarrow Z$$ respectively. Which one of the following choices is true?

The eigen values of the matrix given below are $$\left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr 0 & { - 3} & { - 4} \cr } } \right]$$