Question

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

Answer 1

Answer: 5

$co{t}^{-1}\frac{n}{\pi }>\frac{\pi }{6}$
$\Rightarrow \frac{n}{\pi }<cot\frac{\pi }{6}$
[as $co{t}^{-1}x$ is a decreasing function ]
$\Rightarrow \frac{n}{\pi }<\sqrt{3}$
$\Rightarrow n<\sqrt{3}\pi$
$\Rightarrow n<5.46$
$\Rightarrow$ maximum value of $n$ is $5$