The growth of a medicinal plant of height 1 metre, is 1 cm/day and it is growing straight vertically upward. A man cuts 6 cm from the top, at a regular interval of every 11 days. Its height will be 2 metres after

### Concept & Strategy This is a sequential growth and reduction problem. Care must be taken to distinguish between the continuous daily growth and the discrete periodic cuts. We must track the daily height to see exactly when it hits the threshold. ### Step-by-Step Solution * **Given:** * Initial height = 1 m = 100 cm * Target height = 2 m = 200 cm * Growth rate = 1 cm/day * Cut = 6 cm every 11 days. * **Deduction:** In one 11-day period, the plant grows 11 cm and is then cut by 6 cm. $$\text{Net growth per 11 days} = 11 - 6 = 5 \text{ cm}$$ * **Calculation:** Find how many 11-day cycles it takes to get near 200 cm. After 19 cycles ($19 \times 11 = 209$ days): $$\text{Height} = 100 + 19(5) = 195 \text{ cm}$$ Now, track the daily growth from day 210 onwards (before the 20th cut happens on day 220): * Day 210: 196 cm * Day 211: 197 cm * Day 212: 198 cm * Day 213: 199 cm * Day 214: 200 cm The plant reaches exactly 2 metres on the 214th day. Since 214 is not listed among the options, the correct choice is "None of these". ### Exam Strategy & Shortcut Evaluate the widely accepted "flawed" logic vs. the strict mathematical reality. Flawed logic: Target growth = 100 cm. Net rate = 5 cm / 11 days. Time = $(100 \div 5) \times 11 = 220$ days. Strict math: At day 209, height is 195cm. It grows 1cm/day for 5 days to hit 200cm exactly at day 214. Since 214 is missing, confidently choose "None of these". ### Common Pitfall Blindly assuming the target height is only reached exactly at the end of a full cycle and calculating $(100 \div 5) \times 11 = 220$ days (Option a). This ignores the intra-cycle peak where the plant hits 200 cm organically on day 214 before the next cut occurs. ### Final Answer **Therefore, the correct answer is None of these.**