If 11-2x21-3x=A1-2x+B1-2x2+C1-3x then match the following List-I List-II I) A a) 9 II) B b) -6 III) C c) -2

1(1-2x)2 (1-3x)=A1-2x+B(1-2x)2+C1-3x 1=A(1-3x) (1-2x)+B(1-3x)+C(1-2x)2 x=13 ⇒ 1=C1-232 ⇒ 1=C9 ⇒ C=9 x=12 ⇒ 1=B1-32 ⇒ 1=-B2 ⇒ B=-2 Const ⇒ 1=A+B+C 1=A-2+9 ⇒ A=-6

If 11-2x21-3x=A1-2x+B1-2x2+C1-3x then match the following List-I List-II I) A a) 9 II) B b) -6 III) C c) -2

1(1-2x)2 (1-3x)=A1-2x+B(1-2x)2+C1-3x 1=A(1-3x) (1-2x)+B(1-3x)+C(1-2x)2 x=13 ⇒ 1=C1-232 ⇒ 1=C9 ⇒ C=9 x=12 ⇒ 1=B1-32 ⇒ 1=-B2 ⇒ B=-2 Const ⇒ 1=A+B+C 1=A-2+9 ⇒ A=-6

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$If \frac{1}{{(1 - 2 x)}^{2} (1 - 3 x)} = \frac{A}{1 - 2 x} + \frac{B}{{(1 - 2 x)}^{2}} + \frac{C}{1 - 3 x} then match the following$
$List - I List - II I) A a) 9 II) B b) - 6 III) C c) - 2$

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$I - b, II - c, III - a$

- $I - a, II - b, III - c$

$I - c, II - a, III - b$

$I - c, II - b, III - a$

answer is B.

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Detailed Solution

$\frac{1}{{(1 - 2 x)}^{2} (1 - 3 x)} = \frac{A}{1 - 2 x} + \frac{B}{{(1 - 2 x)}^{2}} + \frac{C}{1 - 3 x} 1 = A (1 - 3 x) (1 - 2 x) + B (1 - 3 x) + C {(1 - 2 x)}^{2} x = \frac{1}{3} \Rightarrow 1 = C {(1 - \frac{2}{3})}^{2} \Rightarrow 1 = \frac{C}{9} \Rightarrow C = 9 x = \frac{1}{2} \Rightarrow 1 = B (1 - \frac{3}{2}) \Rightarrow 1 = \frac{- B}{2} \Rightarrow B = - 2 Const \Rightarrow 1 = A + B + C 1 = A - 2 + 9 \Rightarrow A = - 6$