$\mathrm{KMnO}_4$ acts as an oxidising agent in acidic medium. ' X ' is the difference between the oxidation states of Mn in reactant and product. ' Y ' is the number of ' d ' electrons present in the brown red precipitate formed at the end of the acetate ion test with neutral ferric chloride. The value of $\mathrm{X}+\mathrm{Y}$ is __________.

Some $\mathrm{CO}_2$ gas was kept in a sealed container at a pressure of 1 atm and at 273 K . This entire amount of $\mathrm{CO}_2$ gas was later passed through an aqueous solution of $\mathrm{Ca}(\mathrm{OH})_2$. The excess unreacted $\mathrm{Ca}(\mathrm{OH})_2$ was later neutralized with 0.1 M of 40 mL HCl . If the volume of the sealed container of $\mathrm{CO}_2$ was $x$, then $x$ is ____________ $\mathrm{cm}^3$ (nearest integer). [Given : The entire amount of $\mathrm{CO}_2(\mathrm{~g})$ reacted with exactly half the initial amount of $\mathrm{Ca}(\mathrm{OH})_2$ present in the aqueous solution.]

Only $$2 \mathrm{~mL}$$ of $$\mathrm{KMnO}_4$$ solution of unknown molarity is required to reach the end point of a titration of $$20 \mathrm{~mL}$$ of oxalic acid $$(2 \mathrm{M})$$ in acidic medium. The molarity of $$\mathrm{KMnO}_4$$ solution should be ________ M.

In the reaction of potassium dichromate, potassium chloride and sulfuric acid (conc.), the oxidation state of the chromium in the product is $$(+)$$ _________.