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The number of positive integral solution...

The number of positive integral solution of the equation `tan^(-1)x+cot^(-1)y=tan^(-1)3` is

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
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Assertion (A) : The number of positive integral solutions of x_(1)+x_(2)+x_(3)=10 is 36. Reason (R) : The number positive integral solutions of the equation x_(1)+x_(2)+x_(3)+.......+x_(k)=n is ""^(n-1)C_(k-1) , The correct answer is

tan^(-1)3+"cot"^(-1)3=(pi)/2

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AAKASH SERIES-REVISION EXERCISE-INVERSE TRIGONOMETRIC FUNCTIONS
  1. If alpha = Tan^(-1)((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2)...

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  2. If cos^(-1)[(cos alpha+ cos beta)/(1+cos alpha cos beta)]=2 Tan^(-1)x ...

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  3. The number of positive integral solution of the equation tan^(-1)x+cot...

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  4. 2Tan^(-1)((sqrt(a-b))/(a+b)"tan"x/2)=

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  5. Range of Sin^(-1)x+Cos^(-1)x+Tan^(-1)x is

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  6. Value of underset(n rarr infty )(Lim) sum(r = 1)^(n) Tan^(-1) ((1)/(2r...

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  7. sum(m=1)^(oo)Tan^(-1) ((2m)/(m^(4)+m^(2)+2))=

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

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  9. If a(1),a(2),a(3),...a(n) are in A.P. with common difference d, then t...

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  10. The number of solution of the equation Tan^(-1) sqrt(x^(2)+x)+"Cosec"^...

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  11. The number of real solutions of Tan^(-1)sqrt(x(x+1))+Sin^(-1)sqrt(x^(2...

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  12. If x(1),x(2),x(3) are the roots of x^(3)-6x^(2)+11x-6=0 then cot^(-1)(...

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  13. If A=Tan^(-1)((1)/(7)), B=Cot^(-1)(3) then

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  14. Cot^(-1)(sqrt(Cos alpha))-Tan^(-1)( sqrt(Cos alpha))=x then Sinx=

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  15. If 1/2 le x le 1, then cos^(-1)x+cos^(-1)(x/2+1/2sqrt(3-3x^2)) is equ...

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  16. cos^(-1) sqrt((a-x)/(a-b))= sin^(-1) sqrt((x-b)/(a-b)) is possible if

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  17. The value of lim(|x| to oo) cos(tan^(-1)(sin(tan^(-1)x))) is equal to

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  18. If p gt q gt r gt 0 then sum Cot^(-1)((pq+1)/(p-q))=

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  19. If 0 le x le1 and theta=Sin^(-1) x +Cos^(-1) x-Tan^(-1)x then

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  20. 2"Tan"^(-1)(1)/(5)+"Sec"^(-1)(5 sqrt(2))/(7)+"Tan"^(-1)(1)/(8)=

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