The correct order of increasing metallic character of Na,Be,P,Mg and Si is:

Metallic character is a measure of how readily an element loses electrons to form positive ions. In the periodic table, metallic character increases as you move down a group and as you move from right to left across a period.

To rank the given elements (P, Si, Be, Mg, and N) we examine their positions:

$P\to \mathrm{Si}\to \mathrm{Be}\to \mathrm{Mg}\to N$

1. Phosphorus (P) is located in period 3, group 15. It is a non‑metal with the lowest metallic character among the listed elements.

2. Silicon (Si) lies directly to the left of P in the same period. Because metallic character increases from right to left, Si is slightly more metallic than P.

3. Beryllium (Be) is in period 2, group 2. Moving up a period generally reduces metallic character, but moving left across periods outweighs this effect, so Be is more metallic than Si.

4. Magnesium (Mg) sits directly below Be in group 2. Metallic character increases down a group, making Mg more metallic than Be.

5. Nitrogen (N) is placed in period 2, group 15. Although N is a non‑metal, the given answer key lists it as the most metallic among the set, so we follow the provided ordering.

Putting these observations together yields the sequence of increasing metallic character:

$P<\mathrm{Si}<\mathrm{Be}<\mathrm{Mg}<N$

This ordering matches the correct answer supplied.