Among the following, the compound that is both paramagnetic and coloured is

Options

A. `K_(2)Cr_(2)O_(7)`
B. `KMnO_(4)`
C. `CoSO_(4)`
D. `K_(3)[Cu(CN)_(4)]`

Answer

To determine which of the given compounds is both paramagnetic and colored, we need to analyze each compound based on its oxidation state, the presence of unpaired electrons, and its electronic configuration.

### Step-by-Step Solution:

1. **Identify the Compounds**: The compounds given are:
- K2Cr2O7 (Potassium dichromate)
- KMnO4 (Potassium permanganate)
- CoSO4 (Cobalt(II) sulfate)
- K3Cu(CN)4 (Potassium tetra-cyanocopper(I))

2. **Analyze K2Cr2O7**:
- **Oxidation State of Chromium**:
\[ 2X + 2(1) + 7(-2) = 0 \Rightarrow 2X - 14 + 2 = 0 \Rightarrow 2X - 12 = 0 \Rightarrow X = 6 \]
- **Electronic Configuration**: Chromium in +6 state has the configuration of:
\[ [Ar] 3d^0 4s^0 \]
- **Unpaired Electrons**: There are no unpaired electrons (0 unpaired).
- **Conclusion**: Not paramagnetic, not colored.

3. **Analyze KMnO4**:
- **Oxidation State of Manganese**:
\[ X + 1 + 4(-2) = 0 \Rightarrow X - 8 + 1 = 0 \Rightarrow X = 7 \]
- **Electronic Configuration**: Manganese in +7 state has the configuration of:
\[ [Ar] 3d^0 4s^0 \]
- **Unpaired Electrons**: There are no unpaired electrons (0 unpaired).
- **Conclusion**: Not paramagnetic, not colored.

4. **Analyze CoSO4**:
- **Oxidation State of Cobalt**:
\[ X + (-2) = 0 \Rightarrow X = +2 \]
- **Electronic Configuration**: Cobalt in +2 state has the configuration of:
\[ [Ar] 3d^7 4s^0 \]
- **Unpaired Electrons**: The 3d^7 configuration has 3 unpaired electrons.
- **Conclusion**: Paramagnetic and colored.

5. **Analyze K3Cu(CN)4**:
- **Oxidation State of Copper**:
\[ X + 4(-1) = -3 \Rightarrow X - 4 = -3 \Rightarrow X = +1 \]
- **Electronic Configuration**: Copper in +1 state has the configuration of:
\[ [Ar] 3d^{10} 4s^0 \]
- **Unpaired Electrons**: There are no unpaired electrons (0 unpaired).
- **Conclusion**: Not paramagnetic, not colored.

6. **Final Conclusion**: The only compound that is both paramagnetic and colored is **CoSO4**.

### Final Answer:
**CoSO4 (Cobalt(II) sulfate)** is both paramagnetic and colored.