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Question: Answered & Verified by Expert
If 597 is divided by 52 , then the remainder obtained is
MathematicsBinomial TheoremJEE Main
Options:
  • A 3
  • B 5
  • C 4
  • D 0
Solution:
2868 Upvotes Verified Answer
The correct answer is: 5
We know that, 54=625=52×12+1

54=52λ+1 , where λ is a positive integer.

5424=52λ+124

= C02452λ24+C152λ23+C22452λ2224++C2352λ+C242424 (by binomial theorem)

596=52C0245223λ24+C15223λ2224++C23λ24+1

=a multiple of 52+1

On multiplying both sides by 5 , we get

597=5965=5 a multiple of 52+5

Hence, the required remainder is 5 .

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