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TG EAMCET 2 May 2025 Shift 2 Paper
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© examsnet.com
Question : 3
Total: 160
The value of the greatest positive integer
k
, such that
49
k
+
1
is a factor of
48
(
49
125
+
49
124
+
.
.
.
+
49
2
+
49
+
1
)
is
32
63
65
60
Validate
Solution:
We have,
49
k
+
1
is a factor of
48
(
49
125
+
49
124
+
.
.
.
+
49
2
+
49
+
1
)
Let
S
=
49
125
+
49
124
+
.
.
.
+
49
+
1
⇒
‌
‌
S
=
‌
49
126
−
1
49
−
1
=
‌
49
126
−
1
48
⇒
48
S
=
49
126
−
1
Since,
49
k
+
1
divides
49
126
−
1
∴
k
divides 126 .
⇒
‌
‌
2
k
divides 126
⇒
‌
‌
Greatest possible integer
k
=
63
© examsnet.com
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