Structural Characteristics and Synthesis of Polymers and Biomolecules

To identify the correct statement(s), we evaluate each option individually based on the chemistry of polymers and biomolecules:

1. Option (A): Natural rubber is a linear polymer of isoprene (2-methyl-1,3-butadiene) and is chemically defined as cis-1,4-polyisoprene. The trans-isomer of polyisoprene is known as gutta-percha. Therefore, statement (A) is incorrect.

2. Option (B): Nylon-6 is obtained by heating caprolactam with water at a high temperature. It is a polyamide whose repeating units are held together by amide linkages ($-\mathrm{CONH}-$): $\text{Caprolactam} \xrightarrow{533-543\text{ K, }\mathrm{H_2O}} \left[\mathrm{-NH-(CH_2)_5-CO-}\right]_n$ Therefore, statement (B) is correct.

3. Option (C): Teflon (polytetrafluoroethene or PTFE) is synthesized by the addition polymerization of tetrafluoroethene ($\mathrm{CF_2=CF_2}$) under high pressure in the presence of a free radical or persulphate catalyst: $n\,\mathrm{CF_2=CF_2} \xrightarrow[\text{High pressure}]{\text{Persulphate catalyst}} \left[-\mathrm{CF_2-CF_2}-\right]_n$ Therefore, statement (C) is correct.

4. Option (D): Cellulose is a linear, unbranched polymer consisting exclusively of $\beta$-D-glucose units joined together by $\beta$-1,4-glycosidic linkages (unlike starch/amylose, which consists of $\alpha$-D-glucose units). Therefore, statement (D) is incorrect.

Hence, the correct options are (B) and (C).