Represent the smallest and the largest 7-digit number that can be formed by using any one digit twice, from digits 6, 5, 0, 4, 1 and 2 in Indian system of numeration.

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Solution

The digits given are, 6, 5, 0, 4, 1 and 2.
To make the smallest 7-digit number, 0 must be repeated twice and the digits should be arranged from the smallest to the biggest after the first digit from the left.
<Note: 0 can not be the left most digit as this will not be considered as 7 digit number in that case>
Hence, the smallest 7-digit will be 1002456.
In Indian number system it can be written as 10,02,456.

To make the largest 7-digit number, 6 must be repeated twice and the digits should be arranged from the biggest to the smallest after the first digit from the left.
Hence, the largest 7-digit will be 6654210.
In Indian number system it can be written as 66,54,210.

Suggest Corrections

a.) Largest 4-digit number using any four different digits with digit 5 always at the tens place	i.)1032
b.) Largest 4-digit number formed from the digits 5, 0, and 7 by using any one digit twice	ii.)3399
c.) Smallest 4-digit number using any four different digits with digit 2 always at the ones place	iii.)7750
d.) Smallest 4-digit number formed using the digits 3 and 9 equal number of times	iv.)9857