We know that electric field is negative of the space rate of change of electric potential in a region. i.e.

Option (a) is incorrect as for E =0, V=0 is not the only condition. As we can see from the above equation, electric field is the negative of vector derivative of V that means

if V=constant, then also, E=0.

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Option (b) is incorrect as:

If at a point, the electric potential is zero, it doesn’t imply electric field to be also zero.

Take an example of a dipole where somewhere between the two charges on its axial line, there exists a point where potential is zero but electric field is always non zero and directs in the direction from positive charge to negative charge.

Option (c) is incorrect as if E≠0, it doesn’t mandate the potential to be non-zero. We can take again the example of a dipole where somewhere at a point on its axial line, there exists a point where E≠0 but V=0. So the statement “If E ≠ 0, V cannot be zero” is incorrect.

Option (d) is incorrect as:

If V ≠ 0 (let’s say V= non-zero constant)

Then E=0

Which is contradicted in the given statement.

Thus, none of the options is correct.