A) 27
B) 28
C) 17
D) 14
Correct Answer: C
Solution :
Terms greater than \[5!\] i.e., \[(5!),{{(6!)}^{2}},....,{{(100!)}^{2}}\] is divisible by 100 \[\therefore \] 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. \[\therefore \] Required remainder is 17.You need to login to perform this action.
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