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JEE Main202524 Jan 2025Evening ShiftMathematicsBinomial TheoremActual

Suppose A and B are the coefficients of 30^ th and 12^ th terms respectively in the binomial expansion of (1+x)^ 2 n -1 . If 2 ~A =5 ~B , then n is equal to :

Options

  1. A22
  2. B20
  3. C21
  4. D19

Correct answer

C. 21

Step-by-step solution

aligned & A = ^ 2 n -1 C ₂₉ ~B = ^ 2 n -1 C ₁₁ & 2^ 2 n -1 C ₂₉=5 ^ 2 n -1 C ₁₁ & 2 (2 n -1)! 29!(2 n -30)! =5 (2 n -1)! (2 n -12)!11! & 1 29 12 5 = 1 (2 n -12)(2 n -13) (2 n -29) 2 & 1 30 29 12 = 1 (2 n -12)(2 n -13) (2 n -29) 12 & 2 n -12=30 & n =21 aligned

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