JEE Main20238 Apr 2023Evening ShiftMathematicsBinomial TheoremActual
25 190 - 19 190 - 8 190 + 2 190 is divisible by
Options
- Aneither 14 nor 34
- B14 but not by 34
- C34 but not by 14
- 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,