The correct option is
C The first ionization energies along a period do not vary in a regular manner with increase in atomic number
Let us go through each statement.
The properties of elements are the periodic functions of their atomic numbers
This is the statement of the modern periodic law which is perfectly correct.
Non-metallic elements are lesser in number than metallic elements
This is slightly tricky. If you look at the periodic table, you will notice that all the s-block elements, transition elements, lanthanides, and actinides are all metals. Only a few elements in the p-block are non-metals and rest are metalloids. So, the number of metals is far higher.
The first ionization energies along a period do not vary in a regular manner with increase in atomic number
This is not true. Ionization energy always increases along a period due to increase in effective nuclear charge. It gets more and more difficult to remove an electron.
For transition elements, the sub-shells are filled with electrons monotonically with increase in atomic number
This is generally true in the periodic table. As you go across a period, electrons keep getting added to the sub-shells.