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

The correct option is B 5

$tanx$ is an increasing function since $f^{\prime }\left(x\right)=se{c}^{2}x>0$ for $x\in R.$
$\Rightarrow tan\left({\tan }^{-1}\frac{x}{\pi }\right)<tan\left(\frac{\pi }{3}\right)$
$\Rightarrow \frac{x}{\pi }<\sqrt{3}$
$\Rightarrow x<\pi \times \sqrt{3}$
Thus, the maximum value of $x$ is $5.$