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If cot^(-1)n/pi>pi/6,n in N , then the ...

If `cot^(-1)n/pi>pi/6,n in N ,` then the maximum value of `n` is 6 (b) `7` (c) 5 (d) none of these

A

6

B

7

C

5

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`cot^(-1).(n)/(pi) gt (pi)/(6)`
or `(n)/(pi) lt cot.(pi)/(6)` [as `cot^(-1) x` is a decreasing function]
or `(n)/(pi) lt sqrt3`
or `n lt sqrt3pi`
or `n lt 5.46`
or maximum value of `n` is 5
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