Question

The tens digit of $1!+2!+3!+....+29!$ is:

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

$1!+2!+3!+4!+5!+6!+7!+8!+9!+10!+.......+29!$
Since,$1!+2!+3!+4!=33$
After this for $5!,6!,7!$ all ones place will come 0
Hence ones place of $1!+2!+....29!$ is 3
But for tens place, the tens place will become 0 for factorial of numbers above 10. Hence, we have to add all the tens places for no.s below 10, which is,
$3(till4!)+2(for5!)+2(for6!)+4(for7!)+2(for8!)+8(for9!)$
$=21$
Hence, the tens digit will be $1$ and 2 will be carry.