Question 31 of 43advanced🔧 ApplyShort Answer4 marks

Using all digits from 0 – 9 exactly once (the first digit cannot be 0) to create a 10-digit number, write the — (a) Largest multiple of 5 (b) Smallest even number

(a)
Answer

9876543210

(b)
Answer

1023456798

Explanation

(a) To make the largest multiple of 5, the number must end with 0 or 5. Using 0 at the end and arranging 9,8,7,6,5,4,3,2,1 in descending order gives 9876543210. (b) To make the smallest even number, it must end with an even digit. Using 0 after the leftmost digit '1', and arranging the remaining digits 2,3,4,5,6,7 in ascending order gives 10234567__, and now, to make the answer even, we will write the 8 at the end after 9. Therefore, the final answer is 1023456798. It is the smallest even number with all the digits used once from 0-9.