GATE 2023 BT Q.56: solution and answer

Official answer: 1.0 to 1.2Source: Official answer key, GATE 2023 BT (IIT Kanpur)

1. Convert the Earth–Moon distance into nanometres, the same unit as the base-pair rise: $3,74,000\text{ km}=3.74\times 10^5\text{ km}=3.74\times 10^8\text{ m}=3.74\times 10^{17}\text{ nm}$ (using $1\text{ m}=10^9\text{ nm}$).

2. The distance between two base pairs, $0.34\text{ nm}$, is the rise per base pair along the double helix. So the number of base pairs needed to span a given length is $\frac{\text{length}}{\text{rise per bp}}$.

3. Number of bp $=\frac{3.74\times 10^{17}\text{ nm}}{0.34\text{ nm/bp}}=\frac{3.74}{0.34}\times 10^{17}\text{ bp}=11\times 10^{17}\text{ bp}=1.1\times 10^{18}\text{ bp}$ (since $3.74/0.34=11$).

4. Convert the given mass per 1000 bp to mass per single bp: $\frac{1\times 10^{-18}\text{ gm}}{1000\text{ bp}}=1\times 10^{-21}\text{ gm/bp}$.

5. Total mass $=1\times 10^{-21}\text{ gm/bp}\times 1.1\times 10^{18}\text{ bp}=1.1\times 10^{-3}\text{ gm}$.

6. Convert grams to milligrams ($1\text{ gm}=10^3\text{ mg}$): $1.1\times 10^{-3}\text{ gm}=1.1\text{ mg}$.

7. Rounded to one decimal place, the total amount of DNA required is $1.1\text{ mg}$.