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NDA 2 2024 Maths, question 36

Topic: Algebra

Q36

What is the remainder when 7n−6n7^{n}-6n is divided by 3636 for n=100n=100?

  1. (a) 00
  2. (b) 11Correct answer
  3. (c) 22
  4. (d) 66

Solution.

Answer: (b) 11

  1. Use 7ⁿ=(1+6)ⁿ.
  2. Modulo 36, every binomial term from 6² onward vanishes, so 7ⁿ≡1+6n.
  3. Consequently 7ⁿ−6n≡1 (mod 36), including n=100.