Question

a number becomes a perfect square when we subtract 1 from it. which of given options CANNOT be the last digit number

Answer 1

17-1=16 and 16 square root is 4

Answer 2

If we consider the numbers 1 to 10, the squares of these numbers are  

1, 4, 9, 16, 25, 36, 49, 64, 81 and 100.

This helps us understand that all perfect square numbers end in either 1, 4, 5, 6, 9 or 0.

This automatically implies that a number that does not end in any of the above numbers is not a perfect square number.

In the given problem, the last number is said to be a perfect square number. So, it cannot end in 2, 3, 7 or 8.