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If cot⁻¹(n/π) < π/6, where n ∈ N, then the greatest possible value of n is:

1. 1
2. 5
3. 9
4. None of these

Correct answer: None of these

Solution

cot^-1(n/pi) < pi/6 means n/pi > cot(pi/6) = sqrt(3), so n > pi*sqrt(3) ~ 5.44. Since n can be arbitrarily large, there is no greatest value -> None of these.

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