Which of the following is correct?
`{:(,"Crystal system","Axial distance","Axial angles","Examples"),((1),"Cubic",aneb=c,alpha=betane gamma=90^(@),Cu","KCI),((2),"Monoclinic",aneb=c,alpha=beta=gamma=90^(@),PbCrO_(2)","PbCrO_(4)),((3),"Rhombohedral",a=b=c,alpha=beta=gammane90^(@),CaCO_(3)","NaNO_(3)),((4),"Triclinic",a=b=c,alphanebeta=gammane90^(@),K_(2)Cr_(2)O_(7)","CuSO_(4)","5H_(2)O):}`

Answer

To determine which of the given options regarding crystal systems is correct, we will analyze each option based on the properties of the respective crystal systems.

### Step-by-Step Solution:

1. **Cubic System**:
- **Axial Distances**: In a cubic system, all axial distances are equal, i.e., \( a = b = c \).
- **Axial Angles**: All axial angles are equal to \( 90^\circ \), i.e., \( \alpha = \beta = \gamma = 90^\circ \).
- **Examples**: Common examples include Cu and KCl.
- **Conclusion**: The statement in the question is incorrect because it states \( a \neq b \) and \( \beta \neq \gamma \).

2. **Monoclinic System**:
- **Axial Distances**: In a monoclinic system, the axial distances are unequal, i.e., \( a \neq b \neq c \).
- **Axial Angles**: The angles are such that \( \alpha = \gamma \) and \( \beta \neq 90^\circ \).
- **Examples**: Examples include PbCrO2 and PbCrO4.
- **Conclusion**: This option is also incorrect as it misrepresents the relationship between the axial angles.

3. **Rhombohedral System**:
- **Axial Distances**: In a rhombohedral system, all axial distances are equal, i.e., \( a = b = c \).
- **Axial Angles**: The angles are equal, i.e., \( \alpha = \beta = \gamma \), but they are not equal to \( 90^\circ \).
- **Examples**: Examples include CaCO3 and NaNO3.
- **Conclusion**: This option is correct as it accurately describes the properties of the rhombohedral system.

4. **Triclinic System**:
- **Axial Distances**: In a triclinic system, all axial distances are unequal, i.e., \( a \neq b \neq c \).
- **Axial Angles**: All angles are unequal, i.e., \( \alpha \neq \beta \neq \gamma \), and none are \( 90^\circ \).
- **Examples**: Examples include K2Cr2O7 and CuSO4·5H2O.
- **Conclusion**: This option is incorrect as it does not match the properties of the triclinic system.

### Final Answer:
The correct option is **Option 3: Rhombohedral**.