Q194 / 270 · NDA 2023 (Phase 1) · Mathematics

Paragraph: Consider the sum $\mathrm{S}=0!+1!+2!+3!+4!+\ldots+100!$
Question: If the sum $S$ is divided by 60 , what is the remainder?

  • A
    $1$
  • B
    $3$
  • C
    $17$
  • Correct answer
    D
    $34$

Solution

$\because \quad 5!=120$ $\therefore \quad$ All factorials of 5 or above are divisible by 60 $\therefore \quad$ Remainder will be from $0!+1!+2!+3!+4!=34$

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

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