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The partial fractions of (x^(2))/((x^(2)...

The partial fractions of `(x^(2))/((x^(2)+a^(2))(x^(2)+b^(2)))` are

A

`(1)/(a^(2)+b^(2))[(a^(2))/(x^(2)+a^(2))-(b^(2))/(x^(2)+b^(2))]`

B

`(1)/(b^(2)-a^(2))[(a^(2))/(x^(2)+a^(2))-(b^(2))/(x^(2)+b^(2))]`

C

`(1)/(a^(2)-b^(2))[(a^(2))/(x^(2)+a^(2))-(b^(2))/(x^(2)+b^(2))]`

D

`(1)/(a^(2)-b^(2))[(1)/(x^(2)+a^(2))-(1)/(x^(2)+b^(2))]`

Text Solution

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The correct Answer is:
C
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AAKASH SERIES-PARTIAL FRACTIONS-EXERCISE - II
  1. The partial fractions of (6x^(4)+5x^(3)+x^(2)+5x+2)/(1+5x+6x^(2)) are

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  2. x^(3)/((2x-1)(x+2)(x-3))=A+B/(2x-1)+C/(x+2)+D/(x-3) rArr A =

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  3. The partial fractions of (x^(2))/((x^(2)+a^(2))(x^(2)+b^(2))) are

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  4. The partial fractions of (1)/((x^(2)+9)(x^(2)+16)) are

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  5. (3x^(2)+x+1)/((x-1)^(4))=(A)/(x-1)+(B)/((x-1)^(2))+(C)/((x-1)^(3))+(D)...

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  6. If (x^(4)+24x^(2)+28)/((x^(2)+1)^(3))=A/((x^(2)+1))+B/((x^(2)+1)^(2))+...

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  7. Resolve into Partial Fractions (vi) (x^(2)+13x+15)/((2x+3)(x+3)^(2)...

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  8. The partial fractions of 1/(x^(3)(x+2)) =

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  9. If f(x) is a function of x such that (1)/((1+x)(1+x^(2)))=(A)/(1+x)+(f...

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

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

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

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  13. The partial fractions of ((x+1)^(2))/(x(x^(2)+1)) are

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

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

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

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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 (1)/((1-2x)(1-3x)) is

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

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  20. The number of partial fractions of (x^(3)-3x^(2)+3x)/((x-1)^(5)) is

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