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AP EAMCET2004MathematicsBinomial Theorem

Coefficient of x¹⁰ in the expansion of (2+3 x) e^ -x is

Options

  1. A-26 (10) !
  2. B-28 (10) !
  3. C-30 (10) !
  4. D-32 (10) !

Correct answer

B. -28 (10) !

Step-by-step solution

aligned (2+3 x) e^ -x & & =(2+3 x) (1- x 1 ! + x^2 2 ! - x^3 3 ! + ) aligned Coefficient of x¹⁰ in the above series aligned & = 2 10 ! - 3 9 ! & = 1 10 ! (2-30)= -28 10 ! aligned

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