Q.Which one of the following shows functional isomerism?

Constitutional isomers share a molecular formula but differ in their bonding SEQUENCE -- which atom is actually bonded to which is genuinely different. Five named varieties (a sixth, tautomerism, gets its own full treatment as a separate concept).

Chain (nuclear/skeletal) isomerism -- the carbon skeleton itself differs, straight vs. branched, for the same formula: n-pentane, isopentane (2-methylbutane) and neopentane (2,2-dimethylpropane) are all $C_5H_{12}$.

Position isomerism -- same homologous series, same formula AND same carbon skeleton, but the substituent/functional group/unsaturation sits at a different POSITION: pent-1-ene vs. pent-2-ene (both $C_5H_{10}$); 1-chlorobutane vs. 2-chlorobutane (both $C_4H_9Cl$); pentan-2-one vs. pentan-3-one (both $C_5H_{10}O$).

Functional isomerism -- same formula, entirely DIFFERENT functional groups: propanal (aldehyde) vs. propanone (ketone), both $C_3H_6O$; propanoic acid (acid) vs. methyl acetate (ester), both $C_3H_6O_2$; ethanol vs. dimethyl ether, both $C_2H_6O$, is the single most commonly quoted example.

Metamerism -- a specialised case restricted to compounds whose functional group sits BETWEEN two alkyl groups (ethers, ketones, esters, secondary amines): the isomers share the formula and the same functional group, but the carbon count is split UNEQUALLY between its two sides. Methyl propyl ether vs. diethyl ether (both $C_4H_{10}O$); diethyl ketone vs. methyl propyl ketone vs. methyl isopropyl ketone (all $C_5H_{10}O$). …