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NDA2014MathematicsBinomial TheoremActual

Paragraph: In the expansion of (x^3- 1 x^2 )^n , where n is a positive integer, the sum of the coefficients of x^5 and x¹⁰ is 0. Question: What is the value of the independent term?

Options

  1. A5005
  2. B7200
  3. C-5005
  4. D-7200

Correct answer

C. -5005

Step-by-step solution

Value of the independent term aligned & =- ^n C ₉ (x^3 )^ n-9 ( 1 x^2 )^9=- ¹⁵ C ₉ (x^3 )¹⁵⁻⁹ ( 1 x^2 )^9 & =- ¹⁵ C ₉ x¹⁸⁻¹⁸=- ¹⁵ C ₉ x^0=- ¹⁵ C ₉=- 15! 9! 6! & = -15 14 13 12 11 10 9! 9! 6 5 4 3 2 1 & =-91 55=-5005 aligned

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