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JEE Main Math Class 11 Relations and Functions Part 2 Questions
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© examsnet.com
Question : 12
Total: 95
If
S
=
{
a
∈
R
:
|
2
a
−
1
|
=
3
[
a
]
+
2
{
a
}
}
, where
[
t
]
denotes the greatest integer less than or equal to
t
and
{
t
}
represents the fractional part of
t
, then
72
∑
a
∈
S
a
is equal to _______.
[5 Apr 2024 Shift 1]
Your Answer:
Validate
Solution:
👈: Video Solution
|
2
a
−
1
|
=
3
[
a
]
+
2
{
a
}
|
2
a
−
1
|
=
[
a
]
+
2
a
Case-1
:
a
>
1
2
2
a
−
1
=
[
a
]
+
2
a
[
a
]
=
−
1
∴
a
∈
[
−
1
,
0
)
Reject
Case-2
:
a
<
1
2
−
2
a
+
1
=
[
a
]
+
2
a
a
=
I
+
f
−
2
(
I
+
f
)
+
1
=
I
+
2
I
+
2
f
I
=
0
,
f
=
1
4
∴
a
=
1
4
Hence
a
=
1
4
72
∑
a
∈
S
a
=
72
×
1
4
=
18
© examsnet.com
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