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JEE Main202116 Mar 2021Morning ShiftMathematicsBinomial TheoremActual

If n is the number of irrational terms in the expansion of 3 1 / 4 + 5 1 / 8 60 , then n - 1 is divisible by :

Options

  1. A26
  2. B30
  3. C8
  4. D7

Correct answer

A. 26

Step-by-step solution

3 1 / 4 + 5 1 / 8 60 = C r 60 3 1 / 4 60 - r . 5 1 / 8 r = C r 60 3 60 - r 4 . 5 r 8 For rational terms. r 8 = k ;   0 ≤ r ≤ 60 0 ≤ 8 k ≤ 60 0 ≤ k ≤ 60 8 0 ≤ k ≤ 7 . 5 k = 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 60 - 8 k 4 is always divisible by 4 for all value of k Total rational terms = 8 Total terms = 61 irrational terms = 53 n - 1 = 53 - 1 = 52 52 is divisible by 26 .

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