The state of hybridization of `C_(2), C_(3),C_(5) and C_(6)` of the hydrocarbon,
`underset(7)(CH_(3)) - underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C)- underset(5)(CH) = underset(4)(CH)-underset(3)overset(CH_(3))overset(|)(CH) - C_(2) equiv underset(1)(CH)`
is in the following sequence

Options

A. sp,`sp^(2), sp^(3) and sp^(2)`
B. `sp, sp^(3), sp^(2) and sp^(3)`
C. `sp^(3), sp^(2), sp^(2) and sp`
D. `sp, sp^(2), sp^(2) and sp^(3)`

Answer

To determine the state of hybridization of the carbon atoms C2, C3, C5, and C6 in the given hydrocarbon structure, we will analyze each carbon atom step by step.

### Step-by-Step Solution:

1. **Identify the Carbon Atoms**:
- We need to analyze the hybridization of C2, C3, C5, and C6 from the given structure.

2. **Determine the Hybridization of C2**:
- C2 is involved in a triple bond (C≡C) with another carbon atom.
- In a triple bond, there are 2 pi bonds and 1 sigma bond, which means C2 is making 2 bond pairs.
- Since it forms a total of 2 bond pairs, the hybridization of C2 is **sp**.

3. **Determine the Hybridization of C3**:
- C3 is connected to four other atoms (3 CH3 groups and one C).
- It forms 4 single bonds (one with C2 and three with CH3 groups).
- Since it forms 4 bond pairs, the hybridization of C3 is **sp³**.

4. **Determine the Hybridization of C5**:
- C5 is connected to one carbon (C6) and one hydrogen (H), and it also has a double bond with another carbon.
- It forms 3 bond pairs (1 with C6, 1 with H, and 1 double bond).
- Since it forms 3 bond pairs, the hybridization of C5 is **sp²**.

5. **Determine the Hybridization of C6**:
- C6 is connected to four other atoms (1 with C5 and 3 with CH3 groups).
- It forms 4 single bonds.
- Since it forms 4 bond pairs, the hybridization of C6 is **sp³**.

### Summary of Hybridizations:
- C2: **sp**
- C3: **sp³**
- C5: **sp²**
- C6: **sp³**

### Final Answer:
The sequence of hybridization for C2, C3, C5, and C6 is: **sp, sp³, sp², sp³**.