Factory for synthesis of sugars in autotrophic eukaryotes

The correct option is Chloroplast.

To understand why this is correct, let's break down the biological terms and the functions of the organelles listed:

1. Autotrophic Eukaryotes:
Autotrophic organisms are those that can synthesize their own food (specifically sugars/carbohydrates) from simple inorganic substances like carbon dioxide (${\mathrm{CO}}_2$) and water ($H_{2}O$), typically using light energy. Eukaryotes are organisms whose cells contain a nucleus and other membrane-bound organelles. Examples of autotrophic eukaryotes include plants and algae.

2. Synthesis of Sugars (Photosynthesis):
The process by which sugars are synthesized in autotrophic eukaryotes is called photosynthesis. The general chemical equation representing this synthesis is:
$6{\mathrm{CO}}_2+6H_{2}O+\text{light energy}\to C_6$

3. Role of the Organelles:
Let us evaluate each of the given organelles to identify where this synthesis occurs:

• Chloroplast: These double-membrane organelles contain the green pigment chlorophyll, which absorbs light energy. The chloroplast is the site of photosynthesis, where light energy is converted into chemical energy stored in sugars (like glucose). Thus, it acts as the "factory" for sugar synthesis.
• Mitochondria: These are known as the powerhouses of the cell. Instead of synthesizing sugars, they break down sugars through cellular respiration to generate energy in the form of ATP.
• Ribosome: These are cellular structures responsible for protein synthesis, not sugar synthesis.
• Endoplasmic Reticulum: This organelle is involved in the synthesis and transport of proteins (rough ER) and lipids (smooth ER), but not the primary synthesis of sugars from carbon dioxide.

Therefore, the chloroplast is the cellular organelle that functions as the factory for the synthesis of sugars in autotrophic eukaryotes.