Explanation:

Dipole moment is the measure of the polarity of a molecule. The magnitude of dipole moment is directly proportional to the difference in electronegativity of the atoms forming the bond. If the dipole moments of individual bonds in a molecule cancel out each other, then the net dipole moment of the molecule is zero.

The given compounds are:

a) 1, 1-dichloromethane:

This compound has a dipole moment because the carbon-chlorine bond is polar, and the molecule is not symmetrical. Hence, this molecule has a dipole moment.

b) cis-1, 2-dichloroethene:

This compound has two C-Cl bonds, and the two chlorine atoms are on the same side of the double bond. The dipole moment of each C-Cl bond is in the same direction, and hence, the molecule has a net dipole moment.

c) trans-1, 2-dichloroethene:

This compound has two C-Cl bonds, and the two chlorine atoms are on opposite sides of the double bond. The dipole moment of each C-Cl bond is in the opposite direction, and hence, the molecule has zero net dipole moment.

d) 1-chloroethane:

This compound has a polar C-Cl bond. However, the molecule is symmetrical, and the dipole moments of individual bonds cancel out each other. Hence, the net dipole moment of the molecule is zero.

Therefore, the correct answer is option 'C' trans-1, 2-dichloroethene, which has zero dipole moment due to the cancellation of dipole moments of individual bonds.