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JEE Main Math Class 11 Relations and Functions Part 1 Questions
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© examsnet.com
Question : 46
Total: 100
Let
[
t
]
denote the greatest integer
≤
t
. Then the equation in
x
,
[
x
]
2
+
2
[
x
+
2
]
−
7
=
0
has :
[Sep. 04, 2020 (I)]
exactly two solutions
exactly four integral solutions
no integral solution
infinitely many solutions
Validate
Solution:
The given equation
[
x
]
2
+
2
[
x
]
+
4
−
7
=
0
⇒
[
x
]
2
+
2
[
x
]
−
3
=
0
⇒
[
x
]
2
+
3
[
x
]
−
[
x
]
−
3
=
0
⇒
(
[
x
]
+
3
)
(
[
x
]
−
1
)
=
0
⇒
[
x
]
=
1
or -3
⇒
x
∈
[
−
3
,
−
2
)
∪
[
1
,
2
)
∴
The equation has infinitely many solutions.
© examsnet.com
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