50 '1's, 50 '2's, 50 '3's and 50 '4's are arranged in all possible ways to form 200-digitnumbers. How many of these numbers are perfect squares? A) 100 B) 100100 C) 2001001 D) None of these

Hi Ank,

To verify if a number is perfect square or not, we have to calculate digital root of the number.

Digital root is sum of all the digits of a number, if it is greater than 9, we have to calculate the digital root of the resulting number and so on until we get a single digit number.

No number can be a perfect square, unless its digital root lies among 1, 4, 7 or 9.

Now the digital roots of all the numbers formed will be the same = 50*1+50*2+50*3+50*4 = 500

Therefore, digital root = 5+0+0 = 5.

Therefore, none of the numbers formed are perfect squares.

Hope this helps

Thanks