Given below are the structures of some hydrocarbons. Select the two structures which are related to each other from the given options :

(i) H-C-C-C=C-H (with H substituents)

(ii) H-C-C-C-C-H (with H substituents)

(iii) H-C-C-C-H (cyclic/branched structure with H substituents)

(iv) Cl-C-C-C=C-H (with H substituents)

The NCERT chapter (Section 4.2.1, discussing butane) states: 'We see that both these structures have the same formula $\mathrm{C_4H_{10}}$. Such compounds with identical molecular formula but different structures are called structural isomers.' This is exactly the relationship being tested here.

On working out the molecular formula of each given structure:

• Structure (ii), $\mathrm{H-C-C-C-C-H}$ (with the remaining valencies of carbon satisfied by hydrogen), is a straight (normal) chain of four carbon atoms — this is n-butane, $\mathrm{CH_3-CH_2-CH_2-CH_3}$, molecular formula $\mathrm{C_4H_{10}}$.
• Structure (iii) is a branched-chain arrangement of four carbon atoms — this is iso-butane (2-methylpropane), $\mathrm{(CH_3)_3CH}$, which also has the molecular formula $\mathrm{C_4H_{10}}$.

Both (ii) and (iii) therefore have the identical molecular formula $\mathrm{C_4H_{10}}$ but different arrangements of the carbon skeleton (straight chain vs branched chain), which is the textbook definition of structural isomers. Hence option C is correct.

Why the other options are wrong:

• Option A, (i) and (iv): Structure (i) is an unsaturated hydrocarbon containing a $\mathrm{C=C}$ double bond (an alkene, e.g. but-1-ene, $\mathrm{C_4H_8}$), while structure (iv) is a chloro-substituted unsaturated hydrocarbon containing a chlorine atom (e.g. a chlorobutene, $\mathrm{C_4H_7Cl}$). These have different molecular formulae (one contains Cl, the other does not) and belong to different homologous series/functional groups, so they are not isomers of each other — they are unrelated compounds.
• Option B, (ii) and (iv): Structure (ii) is a saturated hydrocarbon (alkane, $\mathrm{C_4H_{10}}$) with no functional group, whereas structure (iv) is an unsaturated chloro-compound ($\mathrm{C_4H_7Cl}$) containing both a double bond and a halogen substituent. Their molecular formulae differ completely, so there is no isomeric or homologous relationship between them.
• Option D, (i) and (iii): Structure (i) is unsaturated ($\mathrm{C_4H_8}$, contains a $\mathrm{C=C}$ bond) while structure (iii) is the saturated branched-chain isomer of butane ($\mathrm{C_4H_{10}}$). Since one is saturated and the other unsaturated, their molecular formulae differ by $\mathrm{H_2}$, so they cannot be structural isomers of each other.

Only structures with the same molecular formula but different structural arrangement qualify as being 'related' in the sense of isomerism, which uniquely identifies (ii) and (iii), i.e., option C.