First slide

Properties of ITF

Question

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

Moderate

A

6
B

7
C

5
D

10

Solution

$\cot^{- 1} (\frac{n}{π}) > \frac{π}{6} \Rightarrow \frac{n}{π} < \cot (\frac{π}{6}) (∵ c o t^{} i s d e c r e a \sin g) \Rightarrow \frac{n}{π} < \sqrt{3}$
$\Rightarrow n < π \sqrt{3}$
$\Rightarrow n < 5.46$
Maximum value of ‘n’ is 5.

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