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NDA2022MathematicsBinomial TheoremActual

Paragraph: Consider the binomial expansion of (p+q x)^9 : Question: What is the ratio of the coefficients of middle terms in the expansion (when expanded in ascending powers of x )?

Options

  1. Ap q
  2. Bp q
  3. C4 p 5 q
  4. D1 (p q)

Correct answer

B. p q

Step-by-step solution

Middle terms aligned & T₅=T_ 4+1 = ^9 C₄ p^5 q^4 x^4 & T₆=T_ 5+1 = ^9 C₅ p^4 q^5 x^5 & Ratio of coefficients = ^9 C₅ p^5 q^4 ^9 C₄ p^4 q^5 = p q aligned

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