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JEE Main2016MathematicsBinomial TheoremActual

If the number of terms in the expansion of 1 - 2 x + 4 y 2 n , x , y ≠ 0 , is 28 , then the sum of the coefficients of all the terms in this expansion is

Options

  1. A243
  2. B729
  3. C64
  4. D2187

Correct answer

B. 729

Step-by-step solution

1 - 2 x + 4 y 2 n We know, if having three variables then total number of terms would be n + 1 n + 2 2 ⇒ n + 1 n + 2 2 = 28 ∴       n + 1 n + 2   = 56 Which gives n = 6 , and sum of coefficients would be 1 - 2 + 4 6 = 3 6 = 729 .

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