Question

If $co{t}^{-1}\frac{n}{\pi }>\frac{\pi }{6},nϵN$, then the maximum value of n =

• A. 6
• B. 5
• C. 4
• D. None

Answer 1

The correct option is B 5

$co{t}^{-1}\frac{n}{\pi }>\frac{\pi }{6}\Rightarrow \frac{\pi }{6}<co{t}^{-1}\frac{n}{\pi }<\pi ,nϵN$
$\Rightarrow -\infty <\frac{n}{\pi }<\sqrt{3}$ $\Rightarrow -\infty <n<\pi \sqrt{3}$
$\Rightarrow -\infty <n\le 5$ $\Rightarrow$ max. n = 5.