For an integer n, n! = n(n - 1) (n - 2) ..... 3.2.1
Then, 1! + 2! + 3! +.....+ 100!, when divided by 5 leaves remainder
A. 0
B. 1
C. 2
D. 3
Answer: Option D
Solution(By Examveda Team)
Every number from onwards is completely divisible by 5is completely divisible by 5
And,
$$\eqalign{ & = \left( {1 + 2 + 3 \times 2 \times 1 + 4 \times 3 \times 2 \times 1} \right) \cr & = \left( {1 + 2 + 6 + 24} \right) \cr & = 33 \cr} $$
Clearly, 33 when divided by 5 leave a remainder 3
Hence,
When divided by 5 leaves a remainder 3
Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
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