Q100 / 170 · Manipal (MET) 2019 · Mathematics

The remainder obtained when $1!+2!+\ldots+200!$ is divided by 14 is

  • A
    $3$
  • B
    $4$
  • Correct answer
    C
    $5$
  • D
    None of the above

Solution

$\begin{aligned} & (1!+2!+3!+4!+5!+\ldots+200!) \div 14 \\ & =1+2+6+24+120+720+(14 M) \\ & =873+14 M=5+868+14 M \\ & =5+14 \times 62+14 M=5+14(62+M) \end{aligned}$
Hence, when $1!+2!+\ldots+200$ ! is divided by 14 , remainder is 5 .

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

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