An organic compound A has molecular formula `C_(10)H_(17)Br` and it is non-resolvable. A does not decolourize brown colour of bromine water solution. A on treatement with `(CH_(3))_(2 COK//(CH_(3))_(3)COH` yields `B` as majot product. B on treatment with `H_(2)//Pt` yields `(C_(10)H_(16))` which on treatment with `CI_(2)//hv` yields three monochloro derivative. Also B on boiling with acidic permanganate solution yields `C(C_(10)H_(16)O_(3))C`. on heating with sodalime yields `D(C_(9)H_(16)O).D` on reducing with `LiAIH_(4)` followed yields `C(C_(10)H_(16)O_(3)).C` on heating with sodalime yields `D(C_(9)H_(16)O).D` on reducing with `LiAIH_(4)` followed by heating product with concentrated `H_(2)SO_(4)` yields `E(C_(9)H_(16))` as major product. E on treatment with ozone followed by work-up with `Zn-H_(2)O` yields 6-Ketononanal.
Compound A is:

Options

A.
B.
C.
D. none of these

Answer

To determine the structure of the organic compound A with the molecular formula C₁₀H₁₇Br, we will follow a systematic approach based on the information provided in the question.

### Step-by-Step Solution:

1. **Calculate the Degree of Unsaturation (DU)**:
- The formula for calculating the degree of unsaturation is:
\[ DU = \frac{2C + 2 - H - X}{2} \]
where C is the number of carbon atoms, H is the number of hydrogen atoms, and X is the number of halogen atoms.
- For compound A:
- C = 10
- H = 17
- X (Br) = 1
- Plugging in the values:
\[ DU = \frac{2(10) + 2 - 17 - 1}{2} = \frac{20 + 2 - 17 - 1}{2} = \frac{4}{2} = 2 \]
- This indicates that there are 2 degrees of unsaturation, which could be due to either 2 rings, 2 double bonds, or 1 triple bond.

2. **Analyze the Reactivity with Bromine Water**:
- The compound A does not decolorize bromine water, indicating that it does not contain any double bonds or triple bonds. Therefore, the degree of unsaturation must be attributed to rings.

3. **Determine the Structure of Compound A**:
- Since A is non-resolvable (optically inactive), it must have a symmetrical structure.
- Given that there are 2 degrees of unsaturation and the compound is non-resolvable, it is likely that A contains two identical rings that contribute to the non-optical activity.

4. **Propose a Possible Structure**:
- A reasonable structure for compound A is 1,2-dibromo-1,2-dihydroxycyclohexane or a similar bicyclic compound that fits the criteria of having two rings and being non-resolvable.
- The bromine atom can be attached to a carbon that is part of a symmetrical structure, ensuring that the compound remains optically inactive.

5. **Final Structure of Compound A**:
- Based on the analysis, the structure of compound A can be represented as follows:
- A is likely a bicyclic compound with two bromine atoms attached to the same carbon, making it achiral.

### Conclusion:
The compound A is a bicyclic structure that is non-resolvable and does not react with bromine water. The exact structure can be confirmed through further analysis of the products formed in subsequent reactions.