What is the most commonly used technique to separate DNA molecules by…

The correct answer is Option (3) → Gel electrophoresis

Cutting DNA with restriction enzymes gives fragments of different sizes. These are separated by gel electrophoresis. DNA is negatively charged, so in an electric field the fragments move towards the anode through a gel, usually of agarose. The gel acts like a sieve: the smaller the fragment, the farther it moves. The bands are seen after staining with ethidium bromide and exposing to UV light.

Option (1) Chromatography — Incorrect. Chromatography separates the parts of a mixture as they move at different speeds through a medium. The book uses gel electrophoresis, not chromatography, to separate DNA fragments by size.

Option (2) PCR — Incorrect. PCR (polymerase chain reaction) makes many copies of a chosen DNA segment. It amplifies DNA; it does not separate fragments by size.

Option (3) Gel electrophoresis — Correct. Gel electrophoresis separates DNA fragments according to their size through the sieving effect of the agarose gel.

NCERT Extract:
Restriction Enzymes – “… Separation and isolation of DNA fragments : The cutting of DNA by restriction endonucleases results in the fragments of DNA. These fragments can be separated by a technique known as gel electrophoresis. Since DNA fragments are negatively charged molecules they can be separated by forcing them to move towards the anode under an electric field through a medium/matrix. Nowadays the most commonly used matrix is agarose which is a natural polymer extracted from sea weeds. The DNA fragments separate (resolve) according to their size through sieving effect provided by the agarose gel.”