For the reaction, $\mathrm{C} + {\mathrm{xHNO}}_3(\mathrm{conc}.) \to {\mathrm{CO}}_2 + 4{\mathrm{NO}}_2 + {\mathrm{yH}}_2\mathrm{O}$, the value of x and y will be:

Count the atoms of each element on the reactants side as well as the atoms on the products side. If both sides of the equation have an equal number of atoms, the equation is balanced. If not, adjust the coefficients of the molecules until the numbers of atoms for each element on both sides of the equation are equal.

The given equation is:

$\mathrm{C} + {\mathrm{xHNO}}_3(\mathrm{conc}.) \to {\mathrm{CO}}_2 + 4{\mathrm{NO}}_2 + {\mathrm{yH}}_2\mathrm{O}$Lets, balance the atoms of N:

$\mathrm{C} + 4{\mathrm{HNO}}_3(\mathrm{conc}.) \to {\mathrm{CO}}_2 + 4{\mathrm{NO}}_2 + {\mathrm{yH}}_2\mathrm{O}$Now, balance the atoms of H and O:

$\mathrm{C} + 4{\mathrm{HNO}}_3(\mathrm{conc}.) \to {\mathrm{CO}}_2 + 4{\mathrm{NO}}_2 + 2{\mathrm{H}}_2\mathrm{O}$So, the value of x is 4 and y is 2.

The benefit of balancing an equation is that it enables us to determine the quantities of reactants and products that are required. The law of conservation of mass must be followed in every equation. It further asserts that matter cannot be generated or destroyed; rather, it can only change from one form to another.

Hence, the correct answer is 1.