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JEE Main20231 Feb 2023Morning ShiftMathematicsBinomial TheoremActual

The remainder when 19 200 + 23 200 is divided by 49 , is _____ .

Correct answer

0

Step-by-step solution

Solving 19 200 + 23 200 = 21 - 2 200 + 21 + 2 200 = 2 C 0 200 21 200 × 2 0 + C 2 200 21 198 × 2 2 . . . . C 200 200 21 0 × 2 200 Now we know that 21 2 = 441 is divisible by 49 , So rest of the terms will be divisible by 49 So lets consider for 2 C 200 200 21 0 × 2 200 = 2 201 Now rewriting the term 2 201 = 2 3 67 = 7 + 1 67 Now 1 + 7 67 = C 0 67 × 1 + C 1 67 7 + C 2 67 7 2 . . . . . . . . . = 1 + 67 × 7 + 49 k Now when dividing 1 + 7 67 by 49 we consider 1 + 67 × 7 as 49 k is divi

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