See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

# Solution **Step 1: Identify the double bond and stereoisomerism** The molecule contains a $C=C$ double bond with: - Left carbon: $CH_3$ and $H$ groups - Right carbon: $H$ and $-CH_2-CH_2-CHOH-CH_3$ groups Since both carbons of the double bond have two *different* groups attached, **cis-trans (geometrical) isomerism** is possible. $$\text{Geometrical isomers} = \boxed{x = 2}$$ (cis and trans configurations) --- **Step 2: Identify the chiral center and optical isomerism** The carbon bearing the $-OH$ group (in the side chain) is bonded to: - $-OH$ - $-H$ - $-CH_2CH_2-$ (from left) - $-CH_3$ (from right) All four groups are *different*, making this a **chiral center**. $$\text{Optical isomers} = \boxed{y = 2}$$ (R and S enantiomers, or D and L configurations) --- **Step 3: Calculate total stereoisomers** Total stereoisomers = $x \times y = 2 \times 2 = 4$ (2 geometric isomers, each with 2 optical isomers) **Answer: (D) 4 and 2** — The compound exhibits **4 geometrical isomers and 2 optical isomers** due to one double bond (2 geometric forms) and one chiral center (2 optical forms).