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If cot^(-1). (n)/(pi) gt (pi)/(6), n in ...

If `cot^(-1). (n)/(pi) gt (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

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 ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
  1. Find the values of sin (cos−1 3/5)

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  2. The set of values of x, satisfying the equation tan^(2) ( sin^(-1) x) ...

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  3. If cot^(-1). (n)/(pi) gt (pi)/(6), n in N, then the maximum value of n...

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  4. if 6sin1(x^2-6x+12)=2pi, then the value of x, is

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  5. Which of the following is the solution set of the equation sin^-1 x = ...

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  6. If log(2)xge0 then log(1//pi){sin^(-1)((2x)/(1+x^(2)))+2tan^(-1)x} is...

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  7. The value of a for which a x^2+sin^(-1)(x^2-2x+2)+cos^(-1)(x^2-2x+2)=1...

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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. Find the set of values of k for which x^(2) - kx + sin^(-1) ( sin 4) ...

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  11. The set of values of x satisfying abs(sin^(-1)x) le abs(cos^(-1)x) is

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

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  13. The number of real solutions of tan^(-1)sqrt(x(x+1))+sin^(-1)sqrt(x^2+...

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  14. Find the number of real solutions to the equation sqrt(1+cos2x)=sqrt2 ...

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  15. The number of solution of sin{sin^(-1)(log(1//2)x)}+2|cos{sin^(-1)(x...

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  16. The value of "tan"(sin^(-1)("cos"(sin^(-1)x)))"tan"(cos^(-1)(sin(cos^(...

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  17. A value of x satisfying tan(sec^(-1)x)=sin(cos^(-1).(1)/sqrt5) is

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

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  19. If a le sin^(-1)x +cos^(-1)x+tan^(-1)x le b, then:

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  20. If -1lexle0 then sin^(-1)x equals

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