Question

The smallest 5 digit number formed by using the digits 0, 2, 1, 5, 7 only once, is _________.

• A. 01257
• B. 75201
• C. 10257
• D. 75210

Answer 1

The correct option is C 10257

To find the smallest 5-digit number with the given digits, we arrange the digits in ascending order $0<1<2<5<7$

$\begin{array}{ccccc}\text{Ten Thousands}& \text{Thousands}& \text{Hundreds}& \text{Tens}& \text{Ones}\\ 0& 1& 2& 5& 7\\ & & & & \end{array}$

But, by placing zero at the ten thousands place, the formed number comes out to be a 4-digit number, i.e. 1257.
So we can not place zero at the ten thousands place.
We place the smallest digits among the given digits (excluding 0) 1, 2, 5, 7 at the ten thousands place, and then arrange the remaining digits in the ascending order as usual.


$\begin{array}{ccccc}\text{Ten Thousands}& \text{Thousands}& \text{Hundreds}& \text{Tens}& \text{Ones}\\ 1& 0& 2& 5& 7\\ & & & & \end{array}$

Hence, the smallest 5-digit number with the given digits is 10257