1. Identify the species present

Potassium chromate contains the chromate ion: $\mathrm{CrO_4^{2-}}$ In this ion, chromium is in the $+6$ oxidation state.

2. Effect of adding dilute nitric acid

On acidification, chromate ions convert into dichromate ions according to the equilibrium: $2\mathrm{CrO_4^{2-}} + 2\mathrm{H^+} \rightleftharpoons \mathrm{Cr_2O_7^{2-}} + \mathrm{H_2O}$

Since excess dilute nitric acid is added, the equilibrium shifts to the right, producing dichromate ion and water.

3. Check oxidation state change

• In $\mathrm{CrO_4^{2-}}$, Cr is $+6$
• In $\mathrm{Cr_2O_7^{2-}}$, each Cr is also $+6$

So this is not a redox reaction. It is only an acid-base equilibrium shift.

4. Evaluate the options

• A: $\mathrm{Cr_2O_7^{2-}}$ and $\mathrm{H_2O}$ are formed
  ✅ Correct, from $2\mathrm{CrO_4^{2-}} + 2\mathrm{H^+} \rightarrow \mathrm{Cr_2O_7^{2-}} + \mathrm{H_2O}$

• B: $\mathrm{CrO_4^{2-}}$ is reduced to $+3$ state of Cr
  ❌ Incorrect, nitric acid here only acidifies; no reduction to $\mathrm{Cr^{3+}}$ occurs.

• C: $\mathrm{CrO_4^{2-}}$ is oxidized to $+7$ state of Cr
  ❌ Incorrect, chromium remains at $+6$.

• D: $\mathrm{Cr^{3+}}$ and $\mathrm{Cr_2O_7^{2-}}$ are formed
  ❌ Incorrect, $\mathrm{Cr^{3+}}$ is not produced.

5. Final answer

Therefore, the correct option is: $\boxed{A}$