In a uniform electric field,

If all points are at same potential, there cannot exist an electric field, as

$E=-\frac{d V}{d r}$

Hence, (a) is not correct. In a uniform electric field, the lines of force are parallel and equidistant (solid lines). The equipotentials (dotted lines), being perpendicular to lines of force, are also equidistant and parallel.

The distance between A and B is same as that between C and D. But, A and B will have some potential difference, whereas C and D being on the same equipotential, will have no potential difference. Hence, (b) is not correct. 

Points on an equipotential are at the same potential. Hence, (c) is not correct. Hence, answer (d) is correct.