If ∮E.ds=0 over a surface, then :

(i) the electric field inside the surface and on it is zero

(ii) the electric field inside the surface is necessarily uniform

(iii) the number of flux lines entering the surface must be equal to the number of flux lines leaving it

(iv) all charges must necessarily be outside the surface.

Only (iii) is correct

The correct answer is Option 1: Only (iii) is correct

(i) the electric field inside the surface and on it is zero . False. A zero net flux does not mean the field itself is zero. For example, if you place a closed surface in a uniform external electric field, the field is non-zero everywhere, but the net flux is zero because lines enter and leave equally.

(ii) the electric field inside the surface is necessarily uniform. False. The field inside can be non-uniform (e.g., produced by complex charge distributions outside the surface) as long as the net enclosed charge is zero.

(iii) the number of flux lines entering the surface must be equal to the number of flux lines leaving it. True. Total flux is defined as the net number of field lines passing through a surface. If $\oint \vec{E} \cdot d\vec{s} = 0$, the net flux is zero. This physically means that every field line that enters the closed surface must also exit it.

(iv) all charges must necessarily be outside the surface.False. According to Gauss's Law ($\phi = \frac{q_{enclosed}}{\epsilon_0}$), a zero flux means the net enclosed charge is zero. There could be multiple charges inside (like a dipole with $+q$ and $-q$) that sum to zero. Therefore, it is not "necessary" for all charges to be outside.