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BITSAT2024MathematicsBinomial TheoremActual

If the 17^ th and the 18^ th terms in the expansion of (2+a)⁵⁰ are equal, then the coefficient of x³⁵ in the expansion of (a+x)⁻² is

Options

  1. A-35
  2. B3
  3. C36
  4. D-36

Correct answer

D. -36

Step-by-step solution

Given, 17^ th and 18^ th terms in the expansion (2+a)⁵⁰ are equal T₁₇=T₁₈ 50 16 (2)³⁴(a)¹⁶= 50 17 (2)³³(a)¹⁷ a= 50 16 50 17 2=1 Now, coefficient of x³⁵ in the expansion (1+x)⁻²=-36 Coefficient of x^r is (r+1) in (1-x)⁻² .

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