The nature of oxides V$$_2$$O$$_3$$ and CrO is indexed as 'X' and 'Y' type respectively. The correct set of X and Y is:

First, we recall a general rule about the acid-base character of transition-metal oxides. An oxide in a

• low oxidation state of the metal is usually basic,

• intermediate oxidation state is often amphoteric,

• high oxidation state is typically acidic.

Now, we determine the oxidation state in each oxide.

For $$\mathrm{V_2O_3}$$, let the oxidation state of vanadium be $$x$$.

We have $$2x + 3(-2) = 0 \; \Longrightarrow \; 2x - 6 = 0 \; \Longrightarrow \; x = +3.$$ So vanadium is in the $$+3$$ state, which is a low oxidation state. Hence $$\mathrm{V_2O_3}$$ is expected to be basic.

For $$\mathrm{CrO}$$, let the oxidation state of chromium be $$y$$.

We have $$y + (-2) = 0 \; \Longrightarrow \; y = +2.$$ So chromium is in the $$+2$$ state, which is also a low oxidation state. Hence $$\mathrm{CrO}$$ is likewise expected to be basic.

Therefore, in the pair $$\mathrm{V_2O_3}$$ and $$\mathrm{CrO}$$, the oxide $$\mathrm{V_2O_3}$$ (indexed as X) is basic and the oxide $$\mathrm{CrO}$$ (indexed as Y) is also basic.

Hence, the correct answer is Option C.