Question

The smallest 4 digit number having three different digits is
\[\begin{align}
  & A.1102 \\
 & B.1012 \\
 & C.1020 \\
 & D.1002 \\
\end{align}\]

Answer 1

Hint: In this question, we need to find the smallest 4 digit number using three different digits. For this, we will use the three least numbers i.e. 0, 1, and 2. Placing them properly at 4 places for a four-digit number, we obtain our answer.

Complete step by step answer:
Here we need to form the smallest 4 digit number using three different digits.
As we have to use three different digits, so we will use the three smallest digits which are 0, 1, and 2 to form our required number. We have to form a four-digit number so we have to place three digits to 5 places which are ones, tens, hundreds, and thousands. Let us start placing.
For the number to be smallest, we need thousands of places as small as possible. The smallest digit is 0. But as we know, if we place 0 at thousands place our number becomes a three-digit number. So we need to use the next small digit which is 1. Hence we will use one at thousands of places. Next, we need to make hundreds as small as possible. Since 0 is the smallest so we can use it. Hence we will use 0 at hundreds of places. The next place is tens place and we need to make it as small as possible. Since 0 is the smallest digit so we can use it. Hence we will use 0 at tens place. Now to make one’s place smallest, we have to use 2 because this is the last place and we have already used 0 and 1, but we require three different digits. Hence we will use 2 at one's place. Now our number looks like this.
$\dfrac{1}{\text{Thousands}}\dfrac{0}{\text{Hundreds}}\dfrac{0}{\text{Tens}}\dfrac{2}{\text{Ones}}$. Hence this is the required answer. Hence option C is the correct answer.

Note:
 Students should remember that we need to take higher places as small as possible. If we had reversed it and started from one to a thousand, our number would be 2100 which is not the least number required.