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Question

Mathematics Question on Binomial theorem

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

A

9

B

8

C

7

D

6

Answer

9

Explanation

Solution

The correct answer is A:9
1!+2!+3!+4!+......+11!1!+2!+3!+4!+......+11!
=(1!+2!+3!)+(4!+5!+.....+11!)=(1!+2!+3!)+(4!+5!+.....+11!)
=(1+2+6)+(4!+5!+......+11!)=(1+2+6)+(4!+5!+......+11!)
=9+(4!+6!+.....+11!)=9+(4!+6!+.....+11!)
4!,5!........11!4!,5!........11! are divisible by 12
So when you will divide given expression by 12 the remainder will be 9.