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COMEDK2023Morning ShiftMathematicsBinomial TheoremActual

If 49^n + 16n + k is divisible by 64 for n N , then the greatest negative integral value of k is

Options

  1. A- 1
  2. B- 4
  3. C- 3
  4. D- 2

Correct answer

A. - 1

Step-by-step solution

49^n = (1+48)^n = 1 + 48n + n 2 (48)^2 + Since 48^2 = 2304 = 64 36 , all terms from n 2 (48)^2 onwards are divisible by 64. 49^n 1 + 48n 64 49^n + 16n + k 1 + 48n + 16n + k 1 + 64n + k 1 + k 64 For divisibility by 64: 1 + k 0 64 k -1 64 k , -129, -65, -1, 63, 127, Greatest negative integral value of k = -1

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