Answer: Option B
:
B
To find the smallest number wefirst arrange the given digits in ascending order.
0 < 1 < 4 < 6 < 7
Since we cannotwrite a number starting with '0' we have to write it in 2nd position.
So our required order will be 1, 0, 4, 6, 7.
We have to make the smallest 7 digit number using the given digits, so we need 2 more digits.
To make the smallest 7 digit number we will use 1, which is the 2nd smallest digit ($\because$ we have to make the number without repeating 0).
So the smallest 7 digit number using the digits 4, 0, 1, 7, 6 without repeating 0 is1011467.