Write the smallest three-digit numbers using 4,5,6,9 such that the first digit is fixed as 5 (Repetition of digit not allowed).
(a) 564
(b) 546
(c) 569
(d) 596

Hint: After taking 5 as the first fixed digit take the smallest of two digits from three digits. Then there are possibilities of two numbers only choosing the smaller one to get the answer.

Complete step-by-step answer:
In the question we are given 4 digits which are 4,5,6,9 and we have to find the smallest number using digits where a condition is given that 5 is a fixed number to be started.
As we know that 5 is a fixed number, so we have two places left in the number to fill.
The repetition is not allowed in the number so, ‘5’ is omitted. Hence, we are only left with three digits 4, 6, 9. From this we have to choose smaller ones and omit the largest of them.
From 4, 6, 9 we see that 9 is the greatest of them. So, we will omit digit 9.
Now, we have 4, 6 digits to be taken.
Only two numbers can be formed using 4, 5, 6 where 5 is fixed in first place and 4, 6 in the respective two places which are 546 and 564.
In comparison we can say that 546 is smaller than 564.
Hence, the correct option is ‘B’.

Note: Students can also do this by referring to the option and choosing the smallest of them which will be answered,But if the number is of more than 3 digits it is difficult to refer options.