If there were only one type of charge of the universe then

Options

A. `oint_(S) vec(E) .vec(ds) != 0` on any surface
B. `oint_(S) vec(E) .vec(ds) = 0` if the charge is outside the surface
C. `oint_(S) vec(E) .vec(ds)` could not be defined
D. `oint_(S) vec(E) .vec(ds) = (q)/(in_(0))` if charges of magnitude `q` were inside the surface

Answer

B, D

Explanation

As per Gauss's theorem in electrostatics, `oint vec(E) .vec(ds) = (q)/(in_(0))`, where `q` is charge enclosed by the surface. If the charge is outside, `q_(inside) = 0`. Therefore, `oint vec(E) .vec(ds) = 0`
Hence, choices (b) and (d) are correct.