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KEAM 2019 Math Paper
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© examsnet.com
Question : 18
Total: 121
Remainder when
x
=
1
!
+
2
!
+
3
!
+
4
!
+
.
.
.
.
+
100
!
is divided by 240 , is
151
71
153
37
31
Validate
Solution:
For only
r
≥
6
,
r
!
is divisible by 240 as
5
!
<
240
.
Thus, when
x
is divided by 240, Remainder is factorials preceding 6 .
Or
1
!
+
2
!
+
3
!
+
4
!
+
5
!
=
153
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