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JEE Main2004MathematicsBinomial TheoremActual

The coefficient of x^n in expansion of (1+x)(1-x)^n is

Options

  1. A(n-1)
  2. B(-1)^n(1-n)
  3. C(-1)^ n-1 (n-1)^2
  4. D(-1)^ n-1 n

Correct answer

B. (-1)^n(1-n)

Step-by-step solution

Coefficient of x^n in (1+x)(1-x)^n=(1+x) ( ^n C₀- ^n C₁ x+ .+(-1)^ n-1 ^n C_ n-1 x^ n-1 +(-1)^n . . ^n C_n x^n )=(-1)^n ^n C_n+(-1)^ n-1 ^n C_ n-1 =(-1)^n(1-n)

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