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JEE Mains 8-Apr-2023 Shift 1 Solved Paper
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© examsnet.com
Question : 9
Total: 90
Let
S
K
1
+
2
+
.
.
.
+
K
K
and
n
∑
j
=
1
S
j
2
=
n
A
(
Bn
2
+
Cn
+
D
)
, where
A
,
B
,
C
,
D
∈
N
and
A
has least value. Then
[8-Apr-2023 shift 1]
A
+
B
is divisible by
D
A
+
B
=
5
(
D
−
C
)
A
+
C
+
D
is not divisible by
B
A
+
B
+
D
is divisible by 5
Validate
Solution:
S
k
=
k
+
1
2
S
k
2
=
k
2
+
1
+
2
k
4
∴
n
∑
j
−
1
S
j
2
=
1
4
[
n
(
n
+
1
)
(
2
n
+
1
)
6
+
n
+
n
(
n
+
1
)
]
=
n
4
[
(
n
+
1
)
(
2
n
+
1
)
6
+
1
+
n
+
1
]
=
n
4
[
2
n
2
+
3
n
+
1
6
+
n
+
2
]
=
n
4
[
2
n
2
+
9
n
+
13
6
]
=
n
24
[
2
n
2
+
9
n
+
13
]
A
=
24
,
B
=
2
,
C
=
9
,
D
=
13
© examsnet.com
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