Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • How many different six-digit numbers can be formed using the whole numbers less than 8, if repetition is not allowed and ten's position is filled with the square root of n, where n=16? <

How many different six-digit numbers can be formed using the whole numbers less than 8, if repetition is not allowed and ten's position is filled with the square root of n, where n=16?

 

Option: 1

2122


Option: 2

8686


Option: 3

7776


Option: 4

7562


Answers (1)

best_answer

To calculate the number of different six-digit numbers that can be formed using the whole numbers less than 8, with repetition not allowed and the ten's position filled with the square root of 16, we can proceed as follows:

The square root of 16 is 4, so for the ten's position, we have only one option, which is 4.

For the hundred-thousands, ten-thousands, thousands, hundreds, and one's position, we can choose any whole number less than 8 except 4, as repetition is not allowed. The whole numbers less than 8 (excluding 4) are 1, 2, 3, 5, 6, and 7. Therefore, we have six options for each of these positions.

Therefore, the number of different six-digit numbers that can be formed is obtained by multiplying the choices for each position:

Number of choices for the ten's position = 1 (since it is fixed as 4)

Number of choices for the hundred-thousands, ten-thousands, thousands, hundreds, and one's position = 6 (any of the six whole numbers less than 8 except 4)

Total number of different six-digit numbers = Number of choices for the ten's position \times Number of choices for the hundred-thousands position\times Number of choices for the ten-thousands position\times Number of choices for the thousands position \timesNumber of choices for the hundreds position\times Number of choices for the one's position

= 1\times 6 \times6 \times 6\times 6 \times 6

= 7776

Therefore, there are 7776 different six-digit numbers that can be formed using the whole numbers less than 8, with repetition not allowed and the ten's position filled with the square root of 16 (4).

 

Posted by

SANGALDEEP SINGH

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026: JCECEB invites fresh applications for Jharkhand state merit list correction

Latest Question