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Observe the following Lists ul("List -...

Observe the following Lists
`ul("List - I")`
A) If `(3x)/((x-a)(x-b))=(2)/(x-a)+(1)/(x-b)` then `a:b` is
B) If `(x+4)/((x^(2)-4)(x+1))=(A)/(x-2)+(B)/(x+2)+(C)/(x+1)`
then `A+B+C` is
C) If `(2x+1)/((x-1)(x^(2)+1))=(A)/(x-1)+(Bx+C)/(x^(2)+1)` then `C=`
`ul("List - II")`
1) Slope of `x` -axis
2) `sin. (3 pi)/(2)`
3) `{:(" "Lt),(x rarr 0):} (Tan x-Sinx)/(x^(3))`
4) Slope of the line `6x+3y-7=0`
The correct match is

A

4 1 3

B

4 1 3

C

4 1 2

D

2 3 1

Text Solution

Verified by Experts

The correct Answer is:
A
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AAKASH SERIES-PARTIAL FRACTIONS-PRACTICE EXERCISE
  1. ((x+1))/((2x-1)(3x+1))=A/((2x-1))+B/((3x+1)) rArr 16A+9B=

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

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

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  4. If (x^(2)-5x+7)/(x-1)^(3)=A/(x-1)+B/(x-1)^(2)+C/(x-1)^(3) " then " A+B...

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  5. Resolve the following into partial fractions. (3x^(2)-8x^(2) + 10)/(...

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  6. If (2x^(2)+5)/((x+1)^(2)(x-3))=(A)/(x+1)+(B)/((x+1)^(2))+(C)(x-3) then...

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

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

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  9. If (2x^(2)+3x+4)/((x-1)(x^(2)+2))=A/(x-1)+(Bx+C)/(x^(2)+2), " then "B=

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

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

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

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  13. For |x| lt 1, the constant term in the expansion of (1)/((x-1)^(2)(x-2...

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  14. Statement I : (2x-1)/((x+1)(x^(2)+2))=(A)/(x+1)+(3x+c)/(x^(2)+2) the...

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  15. If (x^(2)-10x+13)/((x-1)(x^(2)-5x+6))=(A)/(x-1)+(B)/(x-2)+(C)/(x-3) th...

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  16. If (x^(2)+13x+15)/((x-1)(x^(2)+2))=(A)/(x-1)+(Bx+C)/(x^(2)+2), then th...

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

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  18. Observe the following Lists ul("List - I") A) If (3x)/((x-a)(x-b))...

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  19. a : If 1/((x-2)(x^(2)+1))=A/(x-2)+(Bx+C)/(x^(2)+1) " then "A=1/5, B=-1...

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