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NDA 2 2025 Maths, question 9

Topic: Algebra

Q9

What is the remainder when 5995^{99} is divided by 1313?

  1. (a) 1010
  2. (b) 99
  3. (c) 88Correct answer
  4. (d) 66

Solution.

Answer: (c) 88

  1. Since 5²=25≡−1 (mod 13), 5⁴≡1.
  2. As 99=4×24+3, 5⁹⁹≡5³=125≡8 (mod 13).