Would "carbohydrates" be the correct answer to the nutrient that is the most energy efficient and also to which is the most energy densed?

I do not know what you imply by the terms "energy
efficient" and "energy densed."

In terms of the amount of
energy that nutrients contain, there are three nutrients that can provide energy. These
are carbohydrates, proteins and fats.

Carbohydrates contain
the least amount of energy at 3.75 kilocalories per gram, proteins have a higher amount
of energy at 4 kilocalories per gram and fats have the maximum at 9 kilocalories per
gram.

The body, though, is able to extract energy from
carbohydrates in the easiest manner as compared to proteins and fats. This is the reason
why carbohydrates are first used as a source of energy and only when they get exhausted
does the body move to extracting energy from proteins and fats.