Answer

Verified

479.4k+ views

Hint- Here, we will be choosing the different digits to be placed at different places in order to form the greatest and smallest 4-digit number respectively.

Given, digit 9 is always at hundreds place.

Since, we have to form a 4-digit number so there will be digits at its ones, tens, hundreds and thousands place.

The different digits which can be used to make any number are 0,1,2,3,4,5,6,7,8 and 9.

We already know that in hundreds place there is digit 9, so we are left with digits 0,1,2,3,4,5,6,7,8.

Also, digit 0 cannot be placed at thousands place because we need a 4-digit number not a 3-digit number.

For greatest 4-digit number,

The digit at thousands place should be greatest of 1,2,3,4,5,6,7,8. So, digit 8 should be there. Also, no digit can repeat. So, now we are left with digits 0,1,2,3,4,5,6,7. The digit at tens place should be greatest of 0,1,2,3,4,5,6,7. Hence, digit 7 will be placed at tens place and now we are left with 0,1,2,3,4,5,6. The digit at the ones place will be greatest of 0,1,2,3,4,5,6. Therefore, digit 6 will be placed at the ones place.

Hence, the greatest 4-digit number is 8976.

For smallest 4-digit number,

The digit at thousands place should be the smallest of 1,2,3,4,5,6,7,8. So, digit 1 should be there. Also, no digit can repeat. So, now we are left with digits 0,2,3,4,5,6,7,8. The digit at tens place should be the smallest of 0,2,3,4,5,6,7,8. Hence, digit 0 will be placed at tens place and now we are left with 2,3,4,5,6,7,8. The digit at the ones place will be the smallest of 2,3,4,5,6,7,8. Therefore, digit 2 will be placed at the ones place.

Hence, the smallest 4-digit number is 1902.

Note- These types of problems are solved simply by considering the possibilities of all the cases formed and afterwards going with the one that is asked for. Here, we placed the most appropriate digit at different places in order to make the greatest and smallest 4-digit number provided the given condition also holds.

Given, digit 9 is always at hundreds place.

Since, we have to form a 4-digit number so there will be digits at its ones, tens, hundreds and thousands place.

The different digits which can be used to make any number are 0,1,2,3,4,5,6,7,8 and 9.

We already know that in hundreds place there is digit 9, so we are left with digits 0,1,2,3,4,5,6,7,8.

Also, digit 0 cannot be placed at thousands place because we need a 4-digit number not a 3-digit number.

For greatest 4-digit number,

The digit at thousands place should be greatest of 1,2,3,4,5,6,7,8. So, digit 8 should be there. Also, no digit can repeat. So, now we are left with digits 0,1,2,3,4,5,6,7. The digit at tens place should be greatest of 0,1,2,3,4,5,6,7. Hence, digit 7 will be placed at tens place and now we are left with 0,1,2,3,4,5,6. The digit at the ones place will be greatest of 0,1,2,3,4,5,6. Therefore, digit 6 will be placed at the ones place.

Hence, the greatest 4-digit number is 8976.

For smallest 4-digit number,

The digit at thousands place should be the smallest of 1,2,3,4,5,6,7,8. So, digit 1 should be there. Also, no digit can repeat. So, now we are left with digits 0,2,3,4,5,6,7,8. The digit at tens place should be the smallest of 0,2,3,4,5,6,7,8. Hence, digit 0 will be placed at tens place and now we are left with 2,3,4,5,6,7,8. The digit at the ones place will be the smallest of 2,3,4,5,6,7,8. Therefore, digit 2 will be placed at the ones place.

Hence, the smallest 4-digit number is 1902.

Note- These types of problems are solved simply by considering the possibilities of all the cases formed and afterwards going with the one that is asked for. Here, we placed the most appropriate digit at different places in order to make the greatest and smallest 4-digit number provided the given condition also holds.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths