The remainder obtained when (1 !)²+(2 !)²+(3 !)²+ +(100 !)² is divided by 10² is

Step-by-step solution

Here, terms greater than 5 ! , i.e. (5 !)²,(6 !)², ,(100 !)² is divisible by 100 . For terms (5 !)²,(6 !)², (100 !)² remainder is 0 . Now, consider (1 !)²+(2 !)²+(3 !)²+(4 !)²=1+4+36+576=617 When, 617 is divided by 100 , its remainder is 17 . So, required remainder is 17 .