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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

1

B

5

C

9

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have
`cot^(-1)(n)/(pi)gt(pi)/(6)`
`rarr cot(cot^(-1)(n)/(pi)}ltcot(pi)(6)`
`rarr (n)/(pi)lt sqrt(3)rarr n lt sqrt(3)pi=5.5`
So the maximum value of n is 5
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OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
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  2. The set of values of x, satisfying the equation tan^2(sin^-1x) > 1 is ...

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  8. The value of x that satisfies tan^(-1)(tan -3)=tan^(2)x is

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  9. If cos^(-1)((n)/(2pi)) gt(2pi)/(3) then maximum and minimum values of ...

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  10. The set of values of k for which x^2 - kx + sin^-1 (sin 4) > 0 for all...

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  11. The set of values of x satisfying |sin^(- 1)x|lt|cos^(- 1)x|,is

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  12. If [cot^(-1)x]+[cos^(-1)x]=0 , where [" "] denotes the greatest intege...

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  14. The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^...

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  18. Exhaustive set of values of parameter 'a' so that sin^(-1)x-tan^(-1)x=...

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