Check statement A: $\mathrm{Mn_2O_7}$ is manganese(VII) oxide.

• It is a dark green oily liquid at room temperature.
• Hence, statement A is correct.

Check statement B: $\mathrm{V_2O_4}$ is actually $\mathrm{VO_2}$, where vanadium is in +4 oxidation state.

• On reaction with acids, vanadium(IV) oxide gives vanadyl ion $\mathrm{VO^{2+}}$, not $\mathrm{VO_2^{2+}}$.
• $\mathrm{VO_2^{2+}}$ corresponds to vanadium(V), not vanadium(IV).
• Hence, statement B is incorrect.

Check statement C: $\mathrm{CrO}$ is chromium(II) oxide.

• Lower oxidation state oxides of transition metals are generally basic.
• $\mathrm{CrO}$ is a basic oxide.
• Hence, statement C is correct.

Check statement D: $\mathrm{V_2O_5}$ is vanadium(V) oxide.

• It is an acidic oxide, but it can also show amphoteric behavior and reacts with strong acids to form species such as dioxovanadium(V).
• Therefore, the statement "$\mathrm{V_2O_5}$ does not react with acid" is incorrect.

Conclusion:

• Correct statements are A and C only.
• Therefore, the correct option is C.

Comparison with stored answer:

• Stored correct answer: C
• Derived answer: C
• They agree.