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AP EAMCET202423 May 2024Morning ShiftMathematicsBinomial TheoremActual

For |x| 1 2 , the coefficient of x in the expansion of (1-4 x)^2 (1-2 x^2 )^ 1 / 2 (4-x)^ 3 / 2 is

Options

  1. A61 64
  2. B- 61 64
  3. C69 64
  4. D- 69 64

Correct answer

B. - 61 64

Step-by-step solution

(1-4 x)^2 (1-2 x^2 )^ 1 / 2 (4-x)^ 3 / 2 aligned & = (1+16 x^2-8 x ) (1-2 x^2 )^ 1 / 2 4^ -3 / 2 (1- x 4 )^ -3 / 2 & = 1 8 (1-8 x+16 x^2 ) (1- 2 2 x^2+ ) (1+ 3 x 2 4 ) aligned So, co-efficient of x= 1 8 3 8 -8 = -61 64 .

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