Let V and E denote the gravitational potential and gravitational field at a point. It is possible to have
a) V = 0 and E = 0 b) V = 0 and E $\ne$0 c) V $\ne$0 and E = 0 d) V $\ne$0 and E$\ne$0

$E=-\frac{dV}{dr}$

so when E = 0 , $\frac{dV}{dr}=0$=0 and V = constant value of this constant may be zero or non-zero.

For example, inside a spherical shell, E =0 and V$\ne 0$ , but at a very large distance from a body V =0 and E =0.

Also since mass can produce only negative potential at a point, for a system of particles V can never be zero at a point, V can be zero. So (b) is wrong and (a), (c) and (d) are right.