An optically active hydrocarbon `X` has molecular formula `C_(6)H_(12)`. `X`
on catalytic hydrogenation gives optically inactive `C_(6)H_(14).X`
could be

Options

A. `3-`methyl`-1-`pentene
B. `3-`methyl`-2-`pentene
C. `2-`ethyl`-1-`butene
D. `3-`methylcyclopentene

Answer

To solve the question regarding the optically active hydrocarbon `X` with the molecular formula `C6H12`, which upon catalytic hydrogenation yields the optically inactive compound `C6H14`, we can follow these steps:

### Step 1: Understand the molecular formula
The molecular formula `C6H12` indicates that the compound is likely an alkene, as it follows the general formula for alkenes, `CnH2n`. This means that `X` has a double bond.

**Hint:** Remember that alkenes have the general formula `CnH2n`, while alkanes have `CnH2n+2`.

### Step 2: Identify the characteristics of optically active compounds
An optically active compound must have at least one chiral center, which is a carbon atom bonded to four different groups. This is crucial for the compound to exhibit optical activity.

**Hint:** Look for a carbon atom in the structure that is bonded to four distinct substituents.

### Step 3: Analyze the possible structures of `C6H12`
We need to consider possible structures of `C6H12` that contain a double bond and have a chiral carbon. One possible structure is 3-methyl-1-pentene:

- Structure:
```
CH2=CH-CH(CH3)-CH2-CH3
```

This structure has a chiral carbon at the third position.

**Hint:** Draw the structures of potential candidates and identify chiral centers.

### Step 4: Catalytic hydrogenation of `X`
When `X` is subjected to catalytic hydrogenation (addition of H2), the double bond is converted to a single bond, resulting in an alkane. For 3-methyl-1-pentene, the product will be:

- Product structure:
```
CH3-CH2-CH(CH3)-CH2-CH3
```

This is 3-methylpentane, which is optically inactive because it does not have any chiral centers.

**Hint:** Remember that hydrogenation removes the double bond and can affect the optical activity of the compound.

### Step 5: Evaluate other options
We need to check other possible structures for `C6H12` to ensure they do not yield an optically active compound upon hydrogenation.

- **3-methyl-2-pentene**: This compound does not have a chiral center.
- **2-ethyl-1-butene**: This compound also does not have a chiral center.
- **3-methylcyclopentene**: This compound does not yield a chiral center after hydrogenation.

**Hint:** Compare the structures and check for chiral centers in each option.

### Conclusion
The only structure that satisfies the conditions of being optically active and yielding an optically inactive compound upon hydrogenation is **3-methyl-1-pentene**. Therefore, the answer is:

**Answer:** `X` could be **3-methyl-1-pentene**.