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JEE Main20238 Apr 2023Evening ShiftMathematicsBinomial TheoremActual

25 190 - 19 190 - 8 190 + 2 190 is divisible by

Options

  1. Aneither 14 nor 34
  2. B14 but not by 34
  3. C34 but not by 14
  4. Dboth 14 and 34

Correct answer

C. 34 but not by 14

Step-by-step solution

Given, 25 190 - 19 190 - 8 190 + 2 190 Now 25 190 - 19 190 ,   8 190 ,   2 190 are divisible by 2 , as 25 190 will give remainder as 1 and 19 190 will give remainder as 1 when divided by 2 , so combined 25 190 - 19 190 will give remainder 0 Now, 25 190 - 8 190   &   - 19 190 + 2 190 are divisible by 17 , a n - b n is divisible by a - b if n is even, So given number is divisible by 34 as it is divisible by 2   &   17 both, Now, 25 190 = 7 × 3 + 4 190 , dividing by 7 we get,

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