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AP EAMCET202317 May 2023Evening ShiftMathematicsBinomial TheoremActual

The coefficient of x^2 in the expansion of (1-3 x)^ 1 3 (1+2 x)^ - 1 2 is

Options

  1. A- 3 2
  2. B3 2
  3. C1 2
  4. D- 1 2

Correct answer

B. 3 2

Step-by-step solution

(1-3 x)^ 1 3 (1+2 x)^ - 1 2 aligned & = (1+ 1 3 (-3 x)+ 1 3 ( 1 3 -1 ) 2 ! (-3 x)^2+ ) & . 1+ (- 1 2 )(2 x)+ (- 1 2 ) (- 1 2 -1 ) 2 ! (2 x)^2+ ) & = (1-x-x^2+ ) (1-x+ 3 2 x^2+ ) aligned The coefficient of x^2=1 3 2 +(-1) (-1)+1 (-1)= 3 2 +1-1= 3 2

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