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If (x+1)^(2)/(x^(3)+x)=A/x+(Bx+C)/(x^(2)...

If `(x+1)^(2)/(x^(3)+x)=A/x+(Bx+C)/(x^(2)+1) " then "Sin^(-1)(A/C)=`

A

`pi/6`

B

`pi/4`

C

`pi/3`

D

`pi/2`

Text Solution

Verified by Experts

The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-PARTIAL FRACTIONS-EXERCISE 1
  1. If (2x^(2)+3x+4)/((x-1)(x^(2)+2))=A/(x-1)+(Bx+C)/(x^(2)+2), " then "B=

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  2. If A/x+(Bx)/(x^(2)+1)=(5x^(2)+2)/(x^(3)+x), " then "B=

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  3. If (x+1)^(2)/(x^(3)+x)=A/x+(Bx+C)/(x^(2)+1) " then "Sin^(-1)(A/C)=

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  4. (2x^(3)+x^(2)-5)/(x^(4)-25)=(Ax+B)/(x^(2)-5)+(Cx+1)/(x^(2)+5) rArr (A,...

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  5. If (ax-1)/((1-x+x^(2))(2+x))=x/(1-x+x^(2))-1/(2+x) " then " a=

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  6. If (3x^(3)-2x^(2)-1)/(x^(4)+x^(2)+1)=(Ax+B)/(x^(2)+x+1)+(Cx+D)/(x^(2)+...

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  7. x/((x-1)(x^(2)+1)^(2))=

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  8. 1/((x-3)(x^(2)+1)^(2))=

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  9. (2x-3)/((x-1)(x^(2)+1)^(2))=

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  10. If (1)/((ax+b)(cx+d))=(A)/(ax+b)+(B)/(cx+d) then (1)/((ax+b)^(2)(cx+d)...

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  11. If (1)/((x-a)(x^(2)+b))=(A)/(x-a)+(Bx+C)/(x^(2)+b) then (1)/((x-a)(x^(...

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  12. To find the coefficient of x^(4) in the expansion of (3x)/((x-2)(x-1))...

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  13. The coefficient of x^(3) " in " (5x+6)/((2+x)(1-x)) is

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  14. If abs(x) lt 1 then the coefficient of x^(2) in the expansion of (3x)/...

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  15. The coefficient of x^(n) in the expansion of (1)/(x^(2)-5x+6)"for"|x|l...

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  16. The coefficient of x^(n) in (x-4)/(x^(2)-5x+6) is

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  17. If (x-4)/(x^(2)-5x+6) can be expanded in the ascending powers of x, th...

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  18. The coefficient of x^(n) " in " x/((x-a)(x-b)) is

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  19. The coefficient of x^(n) in (1)/((1-2x)(1-3x)) is

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  20. For |x| lt 1/5, the coefficient of x^(3) in the expansion of (1)/((1-...

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