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If Sigma(r=1)^(2n) sin^(-1) x^(r )=n pi...

If `Sigma_(r=1)^(2n) sin^(-1) x^(r )=n pi, then Sigma__(r=1)^(2n) x_(r )` is equal to

A

n

B

2n

C

`(n(n+1))/(2)`

D

none of these

Text Solution

Verified by Experts

We have
`(pi)/(2)lt sin^(-1)x_(e)le(pi)/(2)for i=1,2…,2n`
`therefore underset(r=1)overset(2n)Sigma sin^(-1)x_(r )=npi`
`rarr sin^(-1) pi_(r ),r=1,2..,2n`
`rarr underset(r=1)overset(2n)Sigma x_(r )=underset(r=1)overset(2n)Sigma 1=2n`
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OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
  1. cos[tan^(-1){tan((15pi)/4)}]

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  2. If Sigma(r=1)^(n) cos^(-1)x(r)=0, then Sigma(r=1)^(n) x(r) equals

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  3. If Sigma(r=1)^(2n) sin^(-1) x^(r )=n pi, then Sigma(r=1)^(2n) x(r )...

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  4. If sin^(- 1)(x-(x^2)/2+(x^3)/4-.....)+cos^(- 1)(x^2-(x^4)/2+(x^6)/4-....

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  5. If sin^(-1)sqrt(x^2+2x + 1) + sec^(-1)sqrt(x^2 + 2x + 1) = pi/2; x!= 0...

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  6. if cos^-1 x > sin^-1 x, then x belongs to the interval

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

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

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  9. if 6sin^-1(x^2-6x+12)=2pi, then the value of x, is

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

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

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

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

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

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

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

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

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

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

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