If the reaction starts with one molecule of DNA, the number of cycles…

The correct answer is Option (3) → 30 cycles

Each cycle of PCR doubles the DNA. Starting from one molecule, after n cycles there are 2ⁿ copies.

2¹⁰ = 1024 ≈ 10³, so 2³⁰ = (2¹⁰)³ ≈ 10⁹ = one billion copies after 30 cycles.

Option (1) 8 cycles — Incorrect. 2⁸ = 256 copies only.

Option (2) 16 cycles — Incorrect. 2¹⁶ = 65,536 copies, far short of a billion.

Option (3) 30 cycles — Correct. In PCR, each cycle doubles the DNA, so after n cycles one molecule gives 2ⁿ copies. 2³⁰ is about 10⁹, so 30 cycles give about one billion copies.

Option (4) 25 cycles — Incorrect. 2²⁵ is about 3.4 crore (3.4 × 10⁷), still about 30 times less than a billion.

NCERT Extract:
Amplification of Gene of Interest Using PCR – “… If the process of replication of DNA is repeated many times, the segment of DNA can be amplified to approximately billion times, i.e., 1 billion copies are made. Such repeated amplification is achieved by the use of a thermostable DNA polymerase (isolated from a bacterium, Thermus aquaticus), which remain active during the high temperature induced denaturation of double stranded DNA.”