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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 (a) 6 (b) `7` (c) 5 (d) none of these

A

A. 6

B

B. 7

C

C. 5

D

D. none of these

Text Solution

Verified by Experts

`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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