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AP EAMCET202420 May 2024Morning ShiftMathematicsBinomial TheoremActual

The coefficient of x^5 in the expansion of (2 x^3- 1 3 x^2 )^5 is

Options

  1. A8
  2. B9
  3. C80 9
  4. D29 3

Correct answer

C. 80 9

Step-by-step solution

General term of (2 x^3- 1 3 x^2 )^5 is T_ r+1 = ^5 C_r (2 x^3 )^ 5-r ( -1 3 x^2 )^r=(2)^ 5-r ( -1 3 )^r ^5 C_r x^ 15-3 r-2 r =(2)^ 5-r ( -1 3 )^r ^5 C_r x^ 15-5 r For coefficient of x^5 put r=2 Coefficient of x^5=2^3 ( -1 3 )^2 C₂= 8 9 5! 2!3! = 80 9

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