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

If `cot^(-1)(n/(pi))>(pi)/6, n in N`, then the maximum value of n is :

A

A. 6

B

B. 7

C

C. 5

D

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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