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

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.)