The heats of combustion of ${CH}_4\left(g\right)$ and $C_2{H}_6\left(g\right)$ are $-890.3$ and $-1560$ $J{mol}^{-1}$ respectively. Which has higher calorific value?

The correct option is A Ethane
Calorific value is the amount of heat produced by complete combustion of 1 Kg of fuel,

so, in case of methane, 16g of methane produce $-890.3Jmo{l}^{-1}$ amount of energy,

so, 1 Kg of metahne produce $-55643.75Jmo{l}^{-1}$

in case of ethane, 28 g produce $-1560Jmo{l}^{-1}$ amount of energy

so, 1 Kg of ethane produce enrgy = $-55714.28Jmo{l}^{-1}$

hence, the energy produce by 1 Kg of ethane is mor than that of methane,

so, Ethane have higher calorific value.