UPSC CAPF (AC) 2024 Paper I · Question 46

Question 46 of the UPSC CAPF (AC) 2024 Paper I (4 August 2024). Try it first, then open the answer and explanation.

1. CAPF 2024 · P-I · Q46 · General Mental Ability · Numbers & Series

   The remainder, when 1 + (1 × 2) + (1 × 2 × 3) + ... + (1 × 2 × 3 × ... × 500) is divided by 8, is

   1. 1
   2. 2
   3. 3
   4. 4

   जब 1 + (1 × 2) + (1 × 2 × 3) + ... + (1 × 2 × 3 × ... × 500) को 8 से विभाजित किया जाता है, तो शेषफल क्या होगा?

   1. 1
   2. 2
   3. 3
   4. 4
   Show answer

   Answer: (1) 1

   उत्तर: (1) 1

   The sum is 1! + 2! + 3! + ... + 500!. From 4! = 24 onwards every term is a multiple of 8, so only 1 + 2 + 6 = 9 matters, and 9 leaves remainder 1 when divided by 8.

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