X and Y are anhydrides of sulphurous and sulphuric acid respectively. The hybridisation state and the shape of X and Y are
`{:("             X","       Y"),("1) "sp^(2)",  angular ",sp^(2)", tetrahedral"),("2) "sp^(2)", angular",sp^(2)", angular"),("3) "sp^(2)", angular",sp^(2)", planar triangular"),("4) "sp^(3)", planar",sp^(3)", planar"):}`

Answer

To solve the problem, we need to determine the hybridization states and shapes of the anhydrides of sulphurous acid (SO₂) and sulphuric acid (SO₃).

### Step-by-step Solution:

1. **Identify the Anhydrides:**
- The anhydride of sulphurous acid (H₂SO₃) is sulfur dioxide (SO₂).
- The anhydride of sulphuric acid (H₂SO₄) is sulfur trioxide (SO₃).

2. **Determine the Hybridization of SO₂:**
- SO₂ has a central sulfur atom bonded to two oxygen atoms with one lone pair of electrons on sulfur.
- The hybridization can be determined by counting the regions of electron density around the sulfur atom:
- 2 bonding pairs (S=O) + 1 lone pair = 3 regions of electron density.
- Therefore, the hybridization of SO₂ is **sp²**.

3. **Determine the Shape of SO₂:**
- With sp² hybridization and one lone pair, the molecular geometry is bent or angular.
- Thus, the shape of SO₂ is **angular**.

4. **Determine the Hybridization of SO₃:**
- SO₃ has a central sulfur atom bonded to three oxygen atoms with no lone pairs on sulfur.
- The hybridization can be determined by counting the regions of electron density:
- 3 bonding pairs (S=O) = 3 regions of electron density.
- Therefore, the hybridization of SO₃ is also **sp²**.

5. **Determine the Shape of SO₃:**
- With sp² hybridization and no lone pairs, the molecular geometry is trigonal planar.
- Thus, the shape of SO₃ is **planar triangular**.

6. **Summarize the Findings:**
- For SO₂ (X): Hybridization = sp², Shape = Angular.
- For SO₃ (Y): Hybridization = sp², Shape = Planar Triangular.

7. **Select the Correct Option:**
- Based on the findings, the correct option is:
- **3) sp², angular; sp², planar triangular**

### Final Answer:
The correct answer is option **3) sp², angular; sp², planar triangular**.