1. Write the structure of hex-1-en-4-yne

Hex-1-en-4-yne means a 6-carbon chain with:

• a double bond between C1 and C2
• a triple bond between C4 and C5

So the structure is:

2. Count the $\pi$ bonds

• One double bond contains $1\pi$ bond.
• One triple bond contains $2\pi$ bonds.

So total $\pi$ bonds:

3. Count the $\sigma$ bonds

Every single bond is one $\sigma$ bond, and each multiple bond also contains one $\sigma$ bond.

(a) C–C bonds

There are 6 carbons in a chain, so total C–C connections are 5:

• $\text{C}_1=\text{C}_2$ contributes $1\sigma$
• $\text{C}_2-\text{C}_3$ contributes $1\sigma$
• $\text{C}_3-\text{C}_4$ contributes $1\sigma$
• $\text{C}_4\equiv\text{C}_5$ contributes $1\sigma$
• $\text{C}_5-\text{C}_6$ contributes $1\sigma$

So C–C sigma bonds =

(b) C–H bonds

Now count hydrogens:

• $\text{C}_1 = \text{CH}_2$ gives 2 C–H bonds
• $\text{C}_2 = \text{CH}$ gives 1 C–H bond
• $\text{C}_3 = \text{CH}_2$ gives 2 C–H bonds
• $\text{C}_4$ in triple bond gives 0 H
• $\text{C}_5$ in triple bond gives 0 H
• $\text{C}_6 = \text{CH}_3$ gives 3 C–H bonds

Total C–H sigma bonds:

(c) Total sigma bonds

4. Final answer

So the correct option is:

C: 13 and 3