Which of the following reactions of methane is incomplete combustion?

The correct option is A $C{H}_4+O_2\to C\left(s\right)+2H_{2}O\left(l\right)$
Alkanes on heating with a regulated supply of dioxygen or air at high pressure and in the presence of suitable catalysts give a variety of oxidation products. This process is called controlled oxidation.
In (c) and (d), methane is heated with a regulated supply of $O_2$/air at high pressure, in the presence of a $M{o}_2{O}_3$ and $Cu$ to give formaldehyde and methanol.
$2C{H}_4+O_2\stackrel{Cu//523K//100atm}{⟶}2C{H}_{3}OHC{H}_4+O_2\underset{\Delta }{\overset{M{o}_2{O}_3}{\to }}HCHO+H_{2}O$

Reaction (b) is complete combustion reaction.
This a process of heating a substance in the presence of sufficient air/$O_2$.
The substance is completely oxidised to $C{O}_2\text{and}{H}_{2}O$ accompanied by evolution of a large amount of heat.

Reaction (a) is incomplete combustion reaction. This reaction is carried out in limited supply of $O_2$ to form coke and water.
Therefore,
$C{H}_4+O_2\to C\left(s\right)+2H_{2}O$ is an incomplete combustion.