Question

If ${\tan }^{-1}\frac{x}{\pi }<\frac{\pi }{3},x\in N$, then the maximum value of x is

• A. 2
• B. 5
• C. 7
• D. None of these

Answer 1

Answer: (B)

We have,
${\tan }^{-1}\frac{x}{\pi }<\frac{\pi }{3}\Rightarrow \tan \left({\tan }^{-1}\frac{x}{\pi }\right)<\tan \frac{\pi }{3}$
$\Rightarrow \frac{x}{\pi }<\sqrt{3}\Rightarrow x<\sqrt{3}\pi =5.5$ (approx.)
$\therefore$ the maximum value of x is 5.