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JEE Main20266 April 2026Morning ShiftMathematicsBinomial TheoremActual

If the coefficients of the middle terms in the binomial expansions of (1 + x)²⁶ and (1 - x)²⁸ , 0 , are equal, then the value of is:

Options

  1. A1
  2. B14 13
  3. C27 7
  4. D7 27

Correct answer

D. 7 27

Step-by-step solution

The expansion of (1 + x)²⁶ has 27 terms. The middle term is T₁₄ . The coefficient of the middle term is ²⁶C₁₃ ¹³ . The expansion of (1 - x)²⁸ has 29 terms. The middle term is T₁₅ . The coefficient of the middle term is ²⁸C₁₄ (- )¹⁴ = ²⁸C₁₄ ¹⁴ . Equating the two coefficients: ²⁶C₁₃ ¹³ = ²⁸C₁₄ ¹⁴ Since 0 , dividing by ¹³ gives: = ²⁶C₁₃ ²⁸C₁₄ Expanding the combinations using factorials: ²⁸C₁₄ = 28! 14! 14! = 28 27 26! 14 13! 14 13! = 28 27 14 14 26! 13! 13! ²⁸C₁₄ = 27 7 ²⁶C₁₃ Substituting this back: = ²⁶C₁₃ 27 7 ²⁶C₁₃

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