Question
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The largest and smallest 4-digit numbers formed by using the digits 4,0,3,7 each only once respectively are:
a)4370, 4037

b)3740, 3047

c)7403, 3704

d)7430, 3047

Answer Verified Verified
Hint: Here, we have to arrange the numbers in ascending and descending order to get the smallest and largest number. We should not keep zero at the first place, keep it in second place for ascending series.

Complete step-by-step answer:

Here, we have the digits 4, 0, 3 and 7. We have to find the largest and smallest number.
 First, let us find the largest number. For that we have to arrange the given numbers in descending order.
We know that descending order and ascending order are the two arrangements of a series of numbers. Descending order means arranging the series of numbers from the largest to the smallest. i.e. the first number should be the largest and the last number should be the smallest.
Here, when we arrange the series 4,0,3,7 in descending order we get, 7, 4, 3, 0.
Therefore, we can say that the largest 4-digit number formed by using the digits 4, 0, 3, 7 each only once respectively is 7430.
Next, let us find the smallest number. For that we have to arrange the given numbers in ascending order.
We know that ascending order means arranging the series of numbers from the smallest to the largest. i.e. the first number should be the smallest and the last number should be the largest.
In the next step, when we arrange the series 4, 0, 3, 7 in ascending order we get, 0, 3, 4, 7.
But when we write it as a number we get 0347, since 0 doesn’t have any value when we put it at the first place, so put 0 at the second place and 3 at the first place. Then we get the series 3,0,4,7
Hence, we can say that the smallest 4-digit number formed by using the digits 4, 0, 3, 7 each only once respectively is 3047.
Therefore the largest and the smallest 4-digit numbers obtained by using the digits each only once are 7430 and 3047 respectively.
So the correct answer for this question is option (d).

Note: When we arrange in the descending order, we get the number 0347, but 0 doesn’t have any value when it is at the first place and we will get a 3-digit number. So we have to put 0 at the second place and 3 at the first place to get the smallest 4-digit number 3047 using the digits 4, 0, 3, 7.