WBJEE · Maths · Mathematical Induction
The remainder obtained when \(1 !+2 !+3 !+\ldots+11 !\) is divided by 12 is
- A 9
- B 8
- C 7
- D 6
Answer & Solution
Correct Answer
(A) 9
Step-by-step Solution
Detailed explanation
Let \(S=1!+2 !+3 !+41+\ldots+11 !\) Here, we see that from \(4 !\) to \(111,\) we alwars get 12 factor, so it is always divisible by 12 Now. \(1 !+2 !+3 !=1+2+6=9\) Hence, when \(S\) is divided by \(12,\) the remainder is 9.
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