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JEE Main202227 Jun 2022Evening ShiftMathematicsBinomial TheoremActual

If the sum of the coefficients of all the positive powers of x , in the binomial expansion of x n + 2 x 5 7 is 939 , then the sum of all the possible integral values of n is

Correct answer

57

Step-by-step solution

Plotting the table for coefficient of x n + 2 x 5 7 and there cumulative sum : Coefficient Commulative sum x 7 n → C 0 7 1 x 6 n - 5 → 2 × C 1 7 1 + 14 x 5 n - 10 → 2 2 × C 2 7 1 + 14 + 84 x 4 n - 15 → 2 3 × C 3 7 1 + 14 + 84 + 280 x 3 n - 20 → 2 4 × C 4 7 1 + 4 + 84 + 280 + 560 = 939 x 2 n - 25 → 2 5 × C 5 7 So, 3 n - 20 ≥ 0   ∩   2 n - 25 < 0   ∩   n ∈ I ∴     7 ≤ n ≤ 12 Sum = 7

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