GATE 2024 IN GA Q.8: solution and answer

Official answer: CSource: Official answer key, GATE 2024 IN (IISc Bengaluru)

1. Read the curve where it meets the vertical gridlines: the risk is about $1.0$ at $0$, $0.45$ at $5000$, $0.18$ at $10000$, $0.10$ at $15000$ and $0.04$ at $20000$ steps/day.

2. The risk reduction over an interval is how far the curve falls across it: $R(\text{start})-R(\text{end})$.

3. Reduction in each 5000-step block: $0\to 5000$: $1.0-0.45\approx 0.55$; $5000\to 10000$: $0.45-0.18\approx 0.27$; $10000\to 15000$: $0.18-0.10\approx 0.08$; $15000\to 20000$: $0.10-0.04\approx 0.06$.

4. (A): $0\to 10000$ gives $1.0-0.18\approx 0.82$ and $10000\to 20000$ gives $0.18-0.04\approx 0.14$. The first reduction is the larger one, so (A) is false.

5. (B): the reduction from $0\to 5000$ ($\approx 0.55$) is much larger than the one from $15000\to 20000$ ($\approx 0.06$), so (B) is false.

6. (C) and (D): from step 3, $0.55>0.27>0.08>0.06$. Each 5000-step block gives a smaller drop than the one before it, because the curve falls steeply at first and then flattens. The largest reduction is $0\to 5000$ and the smallest is $15000\to 20000$, so (C) is true and (D) is false.

7. The exact readings do not change the answer. The curve starts at $1$ and is already below $0.5$ at $5000$ steps/day, so the first block drops by more than $0.5$. Every later block lies between $5000$ and $20000$, so its drop is at most $R(5000)-R(20000)\approx 0.45-0.04=0.41$, which is smaller.