If `(3x)/((x-a)(x-b))=(2)/(x-a)+(1)/(x-b)`then a:b=
1) 1:2
2) -2:1
3) 1:3
4) 3:1

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

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

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

If (3x+4)/(x^(2)-3x+2)=A/(x-2)-B/(x-1) then (A, B) =

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

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

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

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

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

Let a and b be the number of solutions and sum of solutions of (2x)/(x-1)-|x|=(x^2)/(|x-1|) respectively, then a=3 (b) b=1 (c) b=2 (d) a=2