Assertion : In diborane, each B atom is `sp^(2)` hybridised.
Reason : In diborane, the terminal 2-centre-2-electron B-H bonds are called banana bonds.

Explanation

To solve the question regarding the assertion and reason related to diborane, let's break it down step by step.

### Step 1: Understand the Structure of Diborane
Diborane (B₂H₆) consists of two boron (B) atoms and six hydrogen (H) atoms. The bonding in diborane is unique due to the presence of both terminal and bridging hydrogen atoms.

**Hint:** Remember that diborane has a total of 6 hydrogen atoms and 2 boron atoms.

### Step 2: Analyze the Hybridization of Boron
Each boron atom in diborane undergoes hybridization to form bonds. The electronic configuration of boron in its ground state is 1s² 2s² 2p¹. In the excited state, one of the 2s electrons is promoted to the 2p orbital, resulting in the configuration 1s² 2s¹ 2p².

In diborane, each boron atom forms four bonds: three with terminal hydrogen atoms and one with a bridging hydrogen atom. This requires sp³ hybridization, not sp².

**Hint:** Consider how many bonds each boron atom is forming and the type of orbitals involved in bonding.

### Step 3: Identify the Types of Bonds in Diborane
Diborane contains two types of bonds:
1. **Terminal B-H bonds**: These are two-center, two-electron bonds formed between boron and hydrogen atoms.
2. **Bridging B-H bonds**: These are three-center, two-electron bonds where two boron atoms share a hydrogen atom. These bonds are often referred to as "banana bonds" due to their shape.

**Hint:** Distinguish between terminal and bridging bonds and their respective electron sharing.

### Step 4: Evaluate the Assertion and Reason
- **Assertion**: "In diborane, each B atom is sp² hybridized." This is **false** because each boron atom is actually sp³ hybridized.
- **Reason**: "In diborane, the terminal 2-centre-2-electron B-H bonds are called banana bonds." This is also **false** because the terminal bonds are not banana bonds; the banana bonds refer to the bridging bonds.

**Hint:** Check the definitions of hybridization and the types of bonds to confirm their correctness.

### Conclusion
Both the assertion and the reason are incorrect. Therefore, the correct answer is that both statements are false.

**Final Answer**: Both the assertion and the reason are false.