Global warming is due to increase of:

Global warming refers to the long-term rise in Earth's average surface temperature, primarily caused by the accumulation of greenhouse gases in the atmosphere. These gases trap heat from the sun, preventing it from escaping back into space, which leads to a warming effect known as the greenhouse effect.

Now, let us examine the options one by one:

Option A mentions methane and nitrous oxide. Methane (CH$$_4$$) is a potent greenhouse gas, and nitrous oxide (N$$_2$$O) also contributes to global warming. However, carbon dioxide (CO$$_2$$) is the most significant greenhouse gas in terms of total emissions and long-term impact, so this pair is incomplete.

Option B mentions methane and CO$$_2$$. Methane is a major greenhouse gas with high heat-trapping ability, though it has a shorter atmospheric lifetime than CO$$_2$$. Carbon dioxide is the primary driver of global warming, accounting for the largest share of human-induced greenhouse gas emissions from sources like fossil fuel combustion and deforestation. Together, methane and CO$$_2$$ represent two of the most critical gases responsible for global warming.

Option C mentions methane and ozone (O$$_3$$). While ozone in the lower atmosphere (troposphere) acts as a greenhouse gas, its contribution is secondary compared to CO$$_2$$. Ozone is also not directly emitted in large quantities but forms from other pollutants. This pair does not emphasize the dominant role of CO$$_2$$.

Option D mentions methane and carbon monoxide (CO). Carbon monoxide is not a direct greenhouse gas. It can indirectly contribute to warming by reacting to form CO$$_2$$ or ozone, but it is not a primary cause. Methane is relevant, but CO$$_2$$'s absence makes this pair incorrect.

Scientific consensus identifies carbon dioxide as the principal greenhouse gas, with methane being the second most significant. Human activities have substantially increased atmospheric concentrations of both, making them key contributors to global warming. Hence, Option B accurately identifies the increase of methane and CO$$_2$$ as the cause.

So, the answer is Option B.