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UPSC PYQPrelims 2025

Civil Services Examination · Question 67

What is the remainder when 9³ + 9⁴ + 9⁵ + 9⁶ + ... + 9¹⁰⁰ is divided by 6?

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

Answer: (A) 0

Explanation

Every power of 9 leaves remainder 3 on division by 6. There are 98 terms, so the sum ≡ 98 × 3 = 294 ≡ 0 (mod 6). (Answer as per the official UPSC answer key.)