The correct balanced chemical equation showing exothermic reaction in which natural gas burns in air is:

The NCERT chapter (Eq. 1.17) lists the burning of natural gas, $\mathrm{CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)}$, as an example of an exothermic combination-type reaction, i.e. one in which heat is released along with the products. A correct answer must therefore be (i) correctly balanced and (ii) show the release of energy as part of the equation.

Option A — $\mathrm{CH_4 + O_2 \rightarrow CO_2 + 2H_2O}$: unbalanced. Oxygen atoms: LHS has $2$ (in one $\mathrm{O_2}$), RHS needs $2$ (from $\mathrm{CO_2}$) $+ 2$ (from $2\mathrm{H_2O}$) $= 4$. Also does not indicate energy release. Incorrect.

Option B — $\mathrm{CH_4 + 2O_2 \rightarrow 2CO_2 + 2H_2O + Energy}$: unbalanced in carbon. LHS has $1$ carbon atom (in $\mathrm{CH_4}$) but RHS shows $2\mathrm{CO_2}$, i.e. $2$ carbon atoms. Mass/atoms are not conserved, violating the law of conservation of mass stated in the chapter. Incorrect.

Option C — $\mathrm{CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O}$: this is correctly balanced (C: $1=1$; H: $4=4$; O: $4=4$) and is exactly Eq. (1.17) of the chapter, but it does not show that energy is released, so it does not by itself depict the exothermic nature of the reaction, which is what the question specifically asks for. Incorrect as the 'best' choice here.

Option D — $\mathrm{CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O + Energy}$: correctly balanced (same atom count as C) and explicitly shows 'Energy' as a product, matching the chapter's statement that 'burning of natural gas' is an example of an exothermic reaction (reactions in which heat is released along with the formation of products). This is the correct answer.