NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Problems and Solutions

Question 172

Key rule: Ten’s place must be 5 and all digits must be different.

Write the 5-digit pattern:

\( \_\;\_\;\_\;5\;\_ \)

Greatest number

1. Use the largest possible unused digits on the left, from big to small.
2. Available digits (except 5): \(0,1,2,3,4,6,7,8,9\).
3. Ten-thousands: choose \(9\).
4. Thousands: choose \(8\).
5. Hundreds: choose \(7\).
6. Ten’s is fixed: \(5\).
7. Units: next largest unused is \(6\).

Number: \(98756\).

Smallest number

1. Use the smallest possible unused digits, but the first digit cannot be \(0\).
2. Available digits (except 5): \(0,1,2,3,4,6,7,8,9\).
3. Ten-thousands: choose smallest non-zero \(1\).
4. Thousands: now we can use \(0\).
5. Hundreds: next smallest unused is \(2\).
6. Ten’s is fixed: \(5\).
7. Units: next smallest unused is \(3\).

Number: \(10253\).

Checks

• Ten’s place is \(5\) in both numbers.
• All digits are different in both numbers.