The hormone which control the processes of burning of fats, proteins and carbohydrates, with liberation of energy in the body is:

thyroxine

The correct answer is option 1. thyroxine.

Thyroxine, also known as T4, is a hormone produced by the thyroid gland, a butterfly-shaped gland located in the neck. Thyroxine plays a fundamental role in regulating the body's metabolism, which is the process of converting food into energy.

Here's how thyroxine controls the processes of burning fats, proteins, and carbohydrates with the liberation of energy in the body:

1. Metabolism Regulation: Thyroxine regulates the body's metabolic rate, which is the rate at which cells perform chemical reactions to maintain life. It increases the metabolic rate by influencing the activity of enzymes involved in various metabolic pathways.

2. Carbohydrate Metabolism: Thyroxine enhances the breakdown (catabolism) of carbohydrates into glucose through a process called glycolysis. Glucose is then used by cells to produce energy through cellular respiration.

3. Fat Metabolism: Thyroxine stimulates the breakdown of fats (lipids) stored in adipose tissue into fatty acids and glycerol, a process known as lipolysis. These fatty acids can then be oxidized to produce energy in a process called beta-oxidation.

4. Protein Metabolism: Thyroxine influences protein metabolism by promoting protein synthesis in tissues and enhancing the breakdown of proteins (proteolysis) into amino acids. Amino acids can be used for energy production or for the synthesis of new proteins.

5. Energy Production: By increasing the breakdown of carbohydrates, fats, and proteins, thyroxine ultimately leads to the production of ATP (adenosine triphosphate), the primary energy currency of cells. ATP provides the energy necessary for various cellular activities, including muscle contraction, nerve impulses, and biochemical reactions.

Overall, thyroxine plays a crucial role in maintaining energy homeostasis in the body by regulating the metabolism of carbohydrates, fats, and proteins. It ensures that the body has a constant supply of energy to support essential physiological functions and activities.