A compound `(P)` having molecular formula `C_(6)H_(10)` contains two `DU`. It yields `Q(C_(6)H_(12))` when reacts with excess of `H_(2)` of the presence of `Ni`. On ozonolysis `P` gives cyclopentanone and compound `Y`.
`Identify the structure of the compound `P`

Options

A.
B.
C.
D.

Explanation

To identify the structure of compound \( P \) with the molecular formula \( C_6H_{10} \), we can follow these steps:

### Step 1: Determine the Degree of Unsaturation (DU)
The molecular formula \( C_6H_{10} \) indicates that the compound has 2 degrees of unsaturation (DU). The formula for calculating the degree of unsaturation is:
\[ DU = \frac{(2C + 2 - H)}{2} \]
For \( C_6H_{10} \):
\[ DU = \frac{(2 \times 6 + 2 - 10)}{2} = \frac{(12 + 2 - 10)}{2} = \frac{4}{2} = 2 \]
This confirms that \( P \) has 2 degrees of unsaturation.

### Step 2: Analyze the Reaction with Hydrogen
The compound \( P \) reacts with excess hydrogen (\( H_2 \)) in the presence of nickel (Ni) to yield \( Q \) with the formula \( C_6H_{12} \). This indicates that \( P \) has unsaturation (double bonds or rings) that can be hydrogenated to form a saturated compound \( Q \).

### Step 3: Consider Ozonolysis Products
Upon ozonolysis, \( P \) yields cyclopentanone and another compound \( Y \). Cyclopentanone has a five-membered ring with a carbonyl group. This suggests that \( P \) likely contains a ring structure that, when cleaved, produces cyclopentanone.

### Step 4: Structure Elucidation
Given that \( P \) has 2 degrees of unsaturation, one possibility is that it contains a cyclopentene structure (a five-membered ring with one double bond) and another double bond elsewhere in the molecule.

### Step 5: Identify the Structure
The structure of \( P \) can be deduced as follows:
- A cyclopentene ring accounts for one degree of unsaturation.
- An additional double bond (possibly in a chain) accounts for the second degree of unsaturation.

Thus, the structure of \( P \) can be represented as:
\[ \text{Cyclopentene with an additional double bond} \]

### Conclusion
The structure of compound \( P \) is likely to be 1-hexene or a similar compound that contains a cyclopentene ring and one additional double bond.