This cell organelle is responsible to extract energy from carbohydrates to form ATP

The correct option is Mitochondrion.

Here is a step-by-step biological explanation of why the mitochondrion is the organelle responsible for this function:

1. Understanding the Cellular Goal:
Cells require energy to perform various life processes. This energy is stored in the chemical bonds of food molecules, such as carbohydrates (for example, glucose). However, cells cannot use carbohydrates directly. They must convert this chemical energy into a usable cellular energy currency known as Adenosine Triphosphate (ATP).

2. The Process of Cellular Respiration:
The extraction of energy from carbohydrates to synthesize ATP is achieved through a multi-step pathway called cellular respiration. This pathway includes glycolysis, the Krebs cycle (citric acid cycle), and the electron transport chain (oxidative phosphorylation).

3. The Role of the Mitochondrion:
While glycolysis occurs in the cytosol of the cell, the Krebs cycle and the electron transport chain take place inside the mitochondrion. Specifically, the inner membrane of the mitochondrion contains proteins and enzymes that facilitate the electron transport chain, generating the proton gradient required to drive the synthesis of the majority of the cell's ATP.

4. Why Other Options Are Incorrect:
- Lysosome: These contain digestive enzymes that break down waste materials and cellular debris, not synthesize ATP.
- Ribosome: These are the sites of protein synthesis (translation), not energy extraction.
- Chloroplast: These organelles perform photosynthesis to convert solar energy into carbohydrates (chemical energy) in plants and algae, whereas mitochondria break down those carbohydrates to release ATP.