The smallest 4-digit number formed using any four different digits such that 5 is at ones place is ______ .

Options

A. 1025
B. 1205
C. 1250
D. None of these

Answer

To find the smallest 4-digit number formed using any four different digits with the condition that 5 is at the ones place, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the requirements**: We need to form a 4-digit number using four different digits, and the digit 5 must be in the ones place.

2. **Identify the digits available**: The digits we can use are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Since we need four different digits and 5 is already used, we can choose from the remaining digits: 0, 1, 2, 3, 4, 6, 7, 8, and 9.

3. **Determine the thousands place**: The first digit (thousands place) cannot be 0 (as it would make it a 3-digit number). To form the smallest number, we should choose the smallest available digit that is not 0. The smallest digit we can use is 1.

4. **Choose the remaining digits**: After placing 1 in the thousands place and 5 in the ones place, we need to fill the hundreds and tens places with the smallest available digits. The next smallest digit after 1 is 0, and then 2.

5. **Construct the number**: We can now place the digits:
- Thousands place: 1
- Hundreds place: 0
- Tens place: 2
- Ones place: 5

Therefore, the number formed is 1025.

6. **Final answer**: The smallest 4-digit number formed using any four different digits with 5 at the ones place is **1025**.