Given below are two statements :
Statement I: The pentavalent oxide of group-15 element, $$E_2O_5$$, is less acidic than trivalent oxide, $$E_2O_3$$, of the same element.
Statement II : The acidic character of trivalent oxide of group 15 elements, $$E_2O_3$$, decreases down the group.

We need to evaluate both statements about oxides of Group 15 elements.

Statement I: The pentavalent oxide $$E_2O_5$$ is less acidic than the trivalent oxide $$E_2O_3$$ of the same element.

In general, the higher the oxidation state of the central atom, the more acidic the oxide. This is because a higher oxidation state means a greater positive charge on the central atom, which makes it attract electron density from the O-H bond more strongly, facilitating the release of $$H^+$$ ions.

For Group 15 elements:

- In $$E_2O_5$$, the oxidation state of E is +5

- In $$E_2O_3$$, the oxidation state of E is +3

Since higher oxidation state leads to more acidic character, $$E_2O_5$$ is more acidic than $$E_2O_3$$, not less.

Therefore, Statement I is FALSE.

Statement II: The acidic character of trivalent oxide $$E_2O_3$$ decreases down the group.

As we go down Group 15 (N → P → As → Sb → Bi):

- The electronegativity of the element decreases

- The metallic character increases

- The oxides change from acidic → amphoteric → basic

For trivalent oxides specifically:

- $$N_2O_3$$ — acidic

- $$P_2O_3$$ — acidic

- $$As_2O_3$$ — amphoteric

- $$Sb_2O_3$$ — amphoteric

- $$Bi_2O_3$$ — basic

The acidic character clearly decreases down the group.

Therefore, Statement II is TRUE.

The correct answer is Option C: Statement I is false but Statement II is true.