Question

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

• A. $1$
• B. $5$
• C. $9$
• D. $noneofthese$

Answer 1

The correct option is B $5$

Taking $\cot$ on both the sides, we get
$\frac{n}{\pi }<\cot \left(\frac{\pi }{6}\right)$ ($\cot$ is a decreasing function)

$\frac{n}{\pi }<\sqrt{3}$
$n<\pi \left(\sqrt{3}\right)$
$n<5.44$
Hence maximum value of n is 5.