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COMEDK2023MathematicsBinomial Theorem

The coefficient of x²⁹ in the expansion of (1-3 x+3 x^2-x^3 )¹⁵ is

Options

  1. A45 29
  2. B45 28
  3. C- 45 16
  4. D45 30

Correct answer

C. - 45 16

Step-by-step solution

(1-3 x+3 x^2-x^3 )¹⁵= [(1-x)^3 ]¹⁵=(1-x)⁴⁵ So, T_ r+1 = ⁴⁵ C_r(1)^ 45-r (-x)^r For coefficient of x²⁹ , put r=29 Then, T₃₀= 45 29 (1)⁴⁵⁻²⁹(-x)²⁹=- 45 29 x²⁹ Hence, coefficient of x²⁹=- 45 29 and - 45 29 =- 45 16

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