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Official Paper 1: UTET 2019 Paper 1 (English-I/ Hindi-II)

- 3
- 14
- 0
- 5

Option 1 : 3

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**Concept used:**

The number after 6! will be completely divisible by 6

**Calculation:**

3! = 3 × 2 × 1 = 6

4! = 4 × 3 × 2 × 1 = 24

5! = 5 × 4 × 3 × 2 × 1 = 120

The given number is also divisible by 6

Now, 1! + 2! + 3! + ...+ 100! = 3 + 6(1 + 4 + 20 + ...)

Remainder when divided by 6 = 3

**∴ The remainder of the given expression is 3**

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