To determine the number of sigma ($\sigma$) and pi ($\pi$) bonds in pent-2-en-4-yne, we first need to understand its structure.$\\$Pent-2-en-4-yne is an organic compound with the following structure:$\\$CH$_3-$CH$=$CH$-$C$\equiv$CH$\\$Let's analyze the structure step-by-step:$\\$1. The compound has a total of 5 carbon atoms.$\\$2. The suffix "-ene" indicates a double bond, and "-yne" indicates a triple bond.$\\$3. The position numbers (2-en, 4-yne) indicate the location of the double and triple bonds.$\\$Now, let's count the bonds:$\\$• Between $$C$_1$ and $$C$_2:$ a single $\sigma$ bond.$\\$• Between $$C$_2$ and $$C$_3:$ one $\sigma$ bond and one $\pi$ bond (double bond).$\\$• Between $$C$_3$ and $$C$_4:$ a single $\sigma$ bond.$\\$• Between $$C$_4$ and $$C$_5:$ one $\sigma$ bond and two $\pi$ bonds (triple bond).$\\$Additionally, each carbon atom forms bonds with hydrogen atoms to satisfy the tetravalency of carbon:$\\$• $$C$_1$ is bonded to 3 hydrogen atoms (3 $\sigma$ bonds).$\\$• $$C$_2$ is bonded to 1 hydrogen atom (1 $\sigma$ bond).$\\$• $$C$_3$ is bonded to 1 hydrogen atom (1 $\sigma$ bond).$\\$• $$C$_4$ has no hydrogen atoms bonded (0 $\sigma$ bonds).$\\$• $$C$_5$ is bonded to 1 hydrogen atom (1 $\sigma$ bond).$\\$Now, let's count the total number of $\sigma$ and $\pi$ bonds:$\\$Total $\sigma$ bonds:$\\$• 4 $\sigma$ bonds between carbon atoms.$\\$• 6 $\sigma$ bonds with hydrogen atoms.$\\$Total $\sigma$ bonds $= 4 + 6 = 10 \\$Total $\pi$ bonds:$\\$• 1 $\pi$ bond in the double bond.$\\$• 2 $\pi$ bonds in the triple bond.$\\$Total $\pi$ bonds $= 1 + 2 = 3 \\$Therefore, the number of $\sigma$ bonds is 10 and the number of $\pi$ bonds is 3.$\\$This corresponds to Option 1: 10$\sigma$ bonds and 3$\pi$ bonds.