Question

The total number of numbers that can be formed by using digits 1, 2, 3, 4, 5 and 6 exactly once is 6!. How many of them is/are perfect squares?​

Answer 1

Given : The total number of numbers that can be formed by using digits 1, 2, 3, 4, 5 and 6 exactly once is 6!.

To Find :  How many of them is/are perfect squares?​

Solution:

Number formed using digits 1 , 2  , 3 , 4  , 5 and 6

Hence sum of Digits = 1 + 2 + 3 + 4 + 5 + 6  = 21

Hence Any number formed is Divisible by 3

if its a perfect square then it must be divisible by 3²  = 9

but sum 21 is not divisible by 9

Hence  any number formed can not be a perfect square

None of them  is perfect square  

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