Assertion `(A)`: `H_2O` is a linear molecule.
Reason `(R)` : Oxygen is `sp^3` hybridised.

Options

A. If both (A) and (R) are correct and (R) is the correct explanation of (A).
B. If both (A) and (R) are correct but (R) is not the correct explanation of (A).
C. If (A) is correct, but (R) is incorrect.
D. If (A) is incorrect, but (R) is correct.

Explanation

To solve the assertion and reason question regarding water (H₂O), we will analyze both the assertion and the reason step by step.

### Step 1: Analyze the Assertion
The assertion states that "H₂O is a linear molecule."

- **Explanation**: Water (H₂O) is composed of one oxygen atom and two hydrogen atoms. The molecular geometry of water is determined by the arrangement of these atoms and the lone pairs of electrons on the oxygen atom.

- **Conclusion**: The assertion is **false** because H₂O has a bent or V-shaped structure, not a linear one.

### Step 2: Analyze the Reason
The reason states that "Oxygen is sp³ hybridized."

- **Explanation**: In water, the oxygen atom undergoes sp³ hybridization. This means that one s orbital and three p orbitals mix to form four equivalent hybrid orbitals. In the case of water, two of these hybrid orbitals form bonds with hydrogen atoms, while the other two contain lone pairs of electrons.

- **Conclusion**: The reason is **true** because the hybridization of oxygen in water is indeed sp³.

### Step 3: Determine the Relationship Between Assertion and Reason
Now we need to determine whether the reason supports the assertion.

- Since the assertion is false (H₂O is not a linear molecule) and the reason is true (oxygen is sp³ hybridized), the reason does not support the assertion.

### Final Conclusion
- Assertion (A): False
- Reason (R): True

Thus, the correct relationship is that the assertion is incorrect, while the reason is correct.

### Answer Summary
- The assertion that "H₂O is a linear molecule" is **false**.
- The reason that "Oxygen is sp³ hybridized" is **true**.
- Therefore, the correct conclusion is that A is false and R is true.