Write the smallest $5$ - digit number using once the digits $7, 0, 5, 1, 3 .$

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Solution

To write smallest $5$ - digit number the digits from left should be in increasing order.
The order is $0, 1, 3, 5, 7$ but we can't write $0$ at first place as we need to write $5$ - digit number.
The order of digits to write smallest $5$ - digit number is $1, 0, 3, 5, 7 .$
Hence, the smallest $5$ - digit number using the digits $7, 0, 5, 1, 3$ is $10357 .$

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