Q97 / 200 · WBJEE 2014 · Mathematics

The remainder obtained when $1 !+2 !+3 !+\ldots+11 !$ is divided by 12 is

  • Correct answer
    A
    9
  • B
    8
  • C
    7
  • D
    6

Solution

Let $S=1!+2 !+3 !+41+\ldots+11 !$ Here, we see that from $4 !$ to $111,$ we alwars get 12 factor, so it is always divisible by 12 Now. $1 !+2 !+3 !=1+2+6=9$ Hence, when $S$ is divided by $12,$ the remainder is 9.

Hence, the correct answer is option: 'A'.

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