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JEE Main2011MathematicsBinomial TheoremActual

The coefficient of x^7 in the expansion of (1-x-x^2+x^3 )^6 is

Options

  1. A-132
  2. B-144
  3. C132
  4. D144

Correct answer

B. -144

Step-by-step solution

aligned & [1- x - x ^2(1- x ) ]^6=(1- x )^6 (1- x ^2 )^6 & = [ ^6 C ₀- ^6 C ₁ x + ^6 C ₂ x ^2- ^6 C ₃ x ^3+ ^6 C ₄ x ^4- ^6 C ₅ x ^5+ ^6 C ₆ x ^6 ] [ ^6 C ₀- ^6 C ₁ x ^2+ ^6 C ₂ x ^4- ^6 C ₃ x ^6+ . ] aligned Coefficient of x ^7= ^6 C ₁ ^6 C ₃- ^6 C ₃ ^6 C ₂+ ^6 C ₅ ^6 C ₁=120-300+36=-144

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