Question

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

• A. $6$
• B. $7$
• C. $5$
• D. None of these

Answer 1

Answer: (C)

$5$

$co{t}^{-1}\frac{n}{\pi }>\frac{\pi }{6}$

$\frac{n}{\pi }<cot\left(\frac{\pi }{6}\right)$ [ as $co{t}^{-1}x$ is a decreasing function]

$n<\pi \times \sqrt{3}$

$n<\sqrt{3}\pi$

$n<5.16$

so max value of n is $5$