Question

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

• A. $9$
• B. $8$
• C. $7$
• D. $6$

Answer 1

The correct option is A

$9$

Explanation for the correct option:

Find the remainder.

Let $S=1!+2!+3!+\dots ..+11!$

$$\begin{gathered} =(1!+2!+3!)+4!+5!+\dots ..+11! \\ =1+2+6+4!+5!+\dots ..+11! \\ =9+4!+5!+\dots ..+11! \end{gathered}$$

$\left\{4!+5!+\dots ..+11!\right\}$ is divisible by $12.$

When $S$ is divided by $12$, the remainder will be $9$.

Hence, option $A$ is the correct answer.