If two atoms are bonded to a central atom with no lone pairs, how will they be arranged?

Most likely the geometric form of the molecule will be linear.

Explanation:

One possibility is the central atom being an atom with two valance electrons. This will create a liner molecule with no lone pairs of electrons

Another possibility is a central atom being an atom with four valance electrons. If the two atoms each require two bonds like oxygen the result will be a linear molecule with no lone pairs of electrons.