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AP EAMCET201824 Apr 2018Morning ShiftMathematicsBinomial TheoremActual

The coefficient of x^4 in the expansion of (1+x-x^2-x^3 )¹¹ is

Options

  1. A990
  2. B220
  3. C− 220
  4. D− 385

Correct answer

C. − 220

Step-by-step solution

array ll & (1+x-x^2-x^3 )¹¹ & [1(1+x)-x^2(1+x) ]¹¹ & [ (1-x^2 )(1+x) ]¹¹ & [(1-x)(1+x)^2 ]¹¹ & (1-x)¹¹ (1+x)²² array The coefficient of x^4 can be given, aligned & = _ r=0 ^4(-1)^r ¹¹ C_r 22 4-r & ¹¹ C₀ ²² C₄- ¹¹ C₁ ²² C₃ & + ¹¹ C₂ ²² C₂- ¹¹ C₃ ²² C₁+ ¹¹ C₄ ²² C₀ & 7315-16940+12705-3630+330 & 20350-20570=-220 & aligned

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