Chemical nature of the nitrogen oxide compound obtained from a reaction of concentrated nitric acid and P$$_4$$O$$_{10}$$ (in 4 : 1 ratio) is:

When concentrated nitric acid (HNO$$_3$$) reacts with P$$_4$$O$$_{10}$$ in a 4:1 molar ratio, P$$_4$$O$$_{10}$$ acts as a powerful dehydrating agent (it is one of the strongest desiccants known). P$$_4$$O$$_{10}$$ abstracts water from concentrated HNO$$_3$$:

The nitrogen oxide compound produced is dinitrogen pentoxide (N$$_2$$O$$_5$$). The ratio of 4 molecules of HNO$$_3$$ per P$$_4$$O$$_{10}$$ (i.e., 4:1) is consistent with this reaction, as P$$_4$$O$$_{10}$$ removes four water molecules to form metaphosphoric acid HPO$$_3$$ while dehydrating HNO$$_3$$ to N$$_2$$O$$_5$$.

N$$_2$$O$$_5$$ (dinitrogen pentoxide) is the anhydride of nitric acid — it reacts with water to form HNO$$_3$$: $$\text{N}_2\text{O}_5 + \text{H}_2\text{O} \rightarrow 2\text{HNO}_3$$. As an acid anhydride, N$$_2$$O$$_5$$ is acidic in chemical nature.

Therefore, the chemical nature of the nitrogen oxide compound obtained is acidic, which is option 1.