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UPSC PYQPrelims 2025

Civil Services Examination · Question 46

If n is a natural number, then what is the number of distinct remainders of (1^n + 2^n) when divided by 4?

  1. 0
  2. 1
  3. 2
  4. 3
Show answer & explanation

Answer: (C) 2

Explanation

n = 1: 3 leaves remainder 3. n ≥ 2: 2^n is divisible by 4, so the remainder is 1. Two distinct remainders. (Answer as per the official UPSC answer key.)