Which of the following is correct statement :

Options

A. Geometrical isomers are not mirror image isomer.
B. A compound having double bond (restricted bond) always show geometrical isomerism.
C. Acyclic compound having only single bond does not show geometrical isomerism.
D. Cyclodecene can show cis & trans form.

Answer

To determine which of the given statements is correct regarding geometrical isomers and their properties, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement A: Geometrical isomers are not mirror images of each other.**
- Geometrical isomers, also known as cis-trans isomers, occur due to the restricted rotation around a double bond. For example, in a compound with a C=C double bond, if the same groups are on the same side, it is a cis isomer, while if they are on opposite sides, it is a trans isomer.
- To check if they are mirror images, we can visualize placing a mirror in front of the structures. The cis and trans forms will not superimpose on each other, confirming that they are not mirror images.
- **Conclusion:** This statement is **true**.

2. **Statement B: Compounds having double bonds always show geometrical isomers.**
- While double bonds can lead to geometrical isomerism, this is only true if there are two different groups attached to the double-bonded carbons. If both groups are the same (e.g., C=C with two identical groups), then geometrical isomerism cannot occur.
- **Conclusion:** This statement is **false**.

3. **Statement C: Acyclic compounds only have single bonds and do not show geometrical isomers.**
- Acyclic compounds can have double bonds, but if they only have single bonds, they cannot exhibit geometrical isomerism due to the free rotation around single bonds. Therefore, geometrical isomers are not possible in acyclic compounds with only single bonds.
- **Conclusion:** This statement is **true**.

4. **Statement D: Cyclodecalene shows cis and trans forms.**
- Cyclodecalene is a cyclic compound that contains a double bond. It can exhibit cis and trans isomerism depending on the orientation of the substituents around the double bond. The presence of the double bond restricts rotation, allowing for the possibility of cis and trans configurations.
- **Conclusion:** This statement is **true**.

### Final Answer:
The correct statements are **A, C, and D**.

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