Can a molecule have bond dipoles but not have a molecular dipole?

Yes

Explanation: A molecule has a bond dipole but not have a molecular dipole.

Dipole moment:  dipole moment is the product of the distribution of the charge of the molecules and the distance between of the molecules.  

Example:  

lets take an example of   molecule in which two electro negative oxygen atoms are attached with Carbon atom. Oxygen being electro negative will attract the shared pair electrons towards itself and  partial negative charge will create on oxygen atom and partial positive charge on carbon atom C.

due to formation of partial positive and partial negative charges dipole moment is created between oxygen and Carbon bond on both the sides in opposite direction.

Since, the dipole moment acting in opposite direction the net dipole moment in the molecule is zero.

Hence, Yes, a molecule has bond dipoles but not have a molecular dipole.

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