Step 1: Understanding the Concept:
Isomers are molecules with the same molecular formula but different arrangements of atoms. Structural isomers include chain, position, and functional isomers. Stereoisomers include geometric and optical isomers.
Step 2: Detailed Explanation:
A. 2-Methylpropene and but-1-ene: Both have the formula \( C_4H_8 \). 2-Methylpropene has a branched carbon skeleton, whereas but-1-ene is a straight chain. These are chain isomers (III).
B. cis-but-2-ene and trans-but-2-ene: These differ in the spatial arrangement of groups around the double bond. These are geometric isomers, a sub-type of stereoisomers (I).
C. 2-Butanol and diethyl ether: Both have the formula \( C_4H_{10}O \). One is an alcohol and the other is an ether. These are functional group isomers (IV).
D. But-1-ene and but-2-ene: Both are straight-chain butenes, but they differ in the location of the double bond (at C1 vs C2). These are position isomers (II).
Step 3: Final Answer:
The correct matching is A-III, B-I, C-IV, D-II.